opinion: Mr. Justice Stewart
  delivered the opinion of the Court.
  The petitioners and twenty-two others were indicted and tried for conspiracy to evade and defeat the payment of the federal taxes imposed on lottery operations. The petitioners and six others were convicted. Their convictions were affirmed by the Court of Appeals. 259 F. 2d 886. Certiorari was granted to examine the scope of the conspiracy statute in the context of these provisions of the Internal Revenue Code. 358 U. S. 905.
  At the trial it was established by overwhelming evidence that the petitioners had engaged with numerous others in a closely organized and large-scale operation of the numbers game in Atlanta, Georgia, during the years 1954 to 1957, the period covered by the indictment. That activity is a criminal offense under Georgia law. The evidence also established in intricate detail that the participants in this large-scale enterprise had, through a variety of carefully planned stratagems, made every effort to conceal its operation. Finally, the evidence showed that none of the petitioners had paid any of the federal taxes in question. There was no' direct evidence to show that any of the petitioners knew of these taxes.
  In addition to thé conspiracy count, the indictment under which the petitioners were tried also contained two additional counts charging them with the substantive offenses of willful failure to pay the special tax imposed by § 441.1 of the- Internal Revenue Code, in violation of § 72Ó3 of the Code, and. of failure to register as required by § 4412 of the- Code, in violation of § 7272 of the Code. The trial took place subsequent to the announcement of this Court’s decision in United States v. Calamaro, 354 U. S. 351, and the district judge correctly instructed the jury that conviction of the substantive offenses would be justified only as to any defendants found to be “writers,” “bankers,” or to have “a proprietary interest in such lottery operation.” Two of the petitioners, Ingram and Jenkins, were found guilty on both substantive counts and do not question these convictions, conceding the sufficiency of the evidence to show that Ingram was the banker and that Jenkins had a proprietary interest in the enterprise. The evidence showed that the other two petitioners, Smith and Law, were relatively minor clerical functionaries at the headquarters of the operation, and they were acquitted on the substantive counts.
  In sum, what this record presents then is a picture of a large-scale and profitable gambling business conducted in Atlanta over a period of several years by petitioners Ingram and Jenkins. The business involved many participants, including the petitioners Smith and Law. It was a business made criminal by the laws of Georgia, and everyone in the organization participated in trying to keep its operation secret. Ingram and Jenkins were liable for the federal taxes imposed by §§ 4401 and 4411 of the Internal Revenue Code and willfully failed to pay them. They were required by § 4412 of the Code to register with the official in charge of the Internal Revenue District, and they failed to do só. Smith and Law were not themselves subject to any of the taxes here involved. The question presented is whether this factual foundation is sufficient to support a conviction of the petitioners, or any of them, for conspiracy to attempt to evade or defeat federal taxes, “the gravest of offenses against the revenues.” Spies v. United States, 317 U. S. 492, 499. We hold that it was sufficient as to Ingram and. Jenkins, and insufficient as to Smith and Law.
  As to Ingram and Jenkins, the record is clear. They were entrepreneurs in a vast and profitable gambling.business. They were clearly liable for the special taxes and registration requirements that the Federal Government has imposed upon the operators of that kind of business. United States v. Kahriger, 345 U. S. 22. Not only did they willfully fail and néglect to pay these taxes, but they conspired to conceal the operation of the business and the soúrce of .the income upon which the .tax is imposed.
  In Spies v. United States this Court had occasion to consider the quantum and type of evidence required to support a conviction for the substantive offense of attempting to defeat or evade federal taxes as contrasted with the ■ lesser proof required to convict of the misdemeanor of willfully failing to file a return or to pay a tax. It was there said:
  “Willful but passive neglect of the statutory duty may constitute the lesser offense, but to combine with it a willful and positive attempt to evade tax in any manner or to defeat it by any means lifts the offense to the degree o‘f felony.
  “Congress did not define or limit the methods by which a willful attempt to defeat and evade might be accomplished and perhaps did not define lest its effort to do so result in some unexpected limitation. Nor would we by definition constrict the scope of the' Congressional provision that it may be accomplished 'in any manner.’ By way of illustration, and not- by way of limitation, we would think affirmative willful attempt may be inferred from conduct such as keeping a double .set of books,. making false entries or alterations, or false invoices or documents, destruction of books or records, concealment of assets or covering up sources of income, handling of one’s affairs to avoid making the records usual in transactions of the kind, and any conduct, the likely effect of which would be.to mislead or to conceal. If the tax-evasion motive plays any part in such conduct the offense may be made out even though the conduct may also serve other purposes such as concealment of other crime.” 317 U. S., at 499.
  In Spies, the Court was dealing with the substantive offense, not with a conspiracy to commit it. But the evidence of agreement between Ingram and Jenkins to operate this gambling enterprise, which operation made them liable for federal taxes, and to conceal its operation and its income is clear on this record, and is virtually coni ceded by the petitioners. The evidence was sufficient-to support a conclusion that they were engaged not only in a conspiracy to operate and conceal their gambling enterprise, but that they were also parties to an agreement to attempt to defeat or evade the federal taxes imposed upon the operators of such a business.
  As to Smith and Law, the case is quite a different one. While the record clearly supports a finding that Smith and Law were participants in a conspiracy to operate a lottery and to conceal that operation from local law enforcement agencies, we find no warrant for a finding that they were, like Ingram and Jenkins, parties to a conspiracy with a purpose illegal under federal law. Certainly there is nothing in the record to show that Smith and Law knew that Ingram and Jenkins had not paid the taxes, a fact obviously within the knowledge of the latter.
  It is fundamental that a conviction for conspiracy under 18 U. S. C. § 371 cannot be sustained unless there is “proof ef an agreement to commit an offense against the United States.” Pereira v. United States, 347 U. S. 1, 12. There need not,, of course, be proof that the conspirators were aware of the criminality of their objective, but an essential ingredient of the proof was knowledge on the part of Smith and Law that Ingram and Jenkins were liable for federal taxes by reason of the gambling operation. “Without the knowledge, the intent cannot exist.” Direct Sales Co. v. United States, 319 U. S. 703, 711.
  “[Conspiracy to commit a particular substantive offense cannot exist without at least the degree of criminal intent necessary for the substantive offense itself.” The substantive offense which Smith and Law were accused of conspiring to commit was the willful evasion of federal taxes, an offense which, even presuming knowledgé of the tax law, obviously cannot.be committed in the absence of knowledge of willfulness. Spies v. United States, supra. Cf. United States v. Falcone, 311 U. S. 205.
  Indulging, as of course we must, in that view of the evidence most favorable to the Government, we. simply cannot discern adequate foundation in the present record for a finding that Smith and Law had such knowledge of Ingram’s and Jenkins’ wagering tax liability. The record is completely barren of any direct evidence of such knowledge. It was not shown, for example, that any reference had ever, been made by any of the petitioners to possible tax liability, or that they had filed a return or paid a tax in previous years. The Government relied instead upon evidence which) it asserts, circumstantially proved the requisite knowledge on the part of Smith and Law. These circumstances were simply the intimate connection of Smith and Law with the operation of the lottery itself, their cooperation in conducting it secretly, and their apparent knowledge that it was conducted at a profit. The Government points out that not only would payment of the taxes have decreased the profits to be derived from operation of the lottery, but in addition would have required registration, including the names and addresses of the bankers and writers, with the local internal revenue office and the posting of a wagering tax stamp at the place of business. 26 U. S. C. (Supp. V) §§ 4412, 6806 (c). The information contained in the registration would have been available to local law enforcement officials. 26 U. S. C. (Supp. Y) § 6107.
  Yet these circumstances actually are colorless as to the vital issue of knowledge on the part of Smith and Law that their superiors owed' federal wagering taxes. Certainly the secrecy of the operation did not go to show that knowledge. This is not a case where efforts at concealment would be reasonably explainable only in terms of motivation to evade taxation. Here, the criminality of the enterprise under local law provided more than sufficient reason for the secrecy in which it was conducted. A conspiracy, to be sure, may have multiple objectives, United States v. Rabinowich, 238 U. S. 78, 86, and if one of its objectives, even a minor one, be the evasion of federal taxes, the offense is made out, though the primary objective may be concealment of another crime. See Spies v. United States, supra, at 499. But the fact that payment of the federal taxes by Ingram and Jenkins might have resulted in disclosure of the lottery and subsequent prosecution of Smith and Law by local authorities would permit an inference that concealment of the lottery was motivated by a purpose to evade payment of federal taxes only if, independently, there were proof that Smith and Law knew of the tax liability. Evidence that Smith and Law might have wanted the taxes to be evaded if they .had known of them, and that they engaged in conduct which -could have been in furtherance of a plan to evade the taxes if they had known of them, is not evidence that they did know of them.
  What was said in Direct Sales Co. v. United States on behalf of a unanimous Court is of particular relevance here:
  “Without the knowledge, the intent cannot exist. . . . Furthermore, to establish the intent, the evidence of knowledge must be clear, not equivocal..... This, because charges of conspiracy are not to be made out by piling inference upon inference, thus fashioning ... a dragnet to draw in all substantive crimes.” 319 U. S., at 711.
  Smith and Law were not liable for the wagering tax. United States v. Calamaro, supra. They could not, therefore, have been convicted of the crime which they were charged with having conspired to commit. To sustain their conviction on this record would make of the crime of conspiracy just that “dragnet to draw in all substantive crimes” against which the Court warned in Direct Sales. Cf. Gebardi v. United States, 287 U. S. 112.
  Accordingly, while affirming the convictions of Ingram and Jenkins, we hold that the motions.for acquittal of Smith and Law should have been sustained by the District Court, and that the Court of Appeals was in error in affirming their convictions.
  Judgment accordingly.*
  • Mr. Justice Black took no part in the consideration or decision of this case.
  Section 4401 of the Internal Revenue Code of 1954 provides:
  “(a) Wagers. — There shall be imposed on wagers, as defined in section 4421, an excise tax equal to 10 percent of the amount thereof.
  “(c) Persons liable for tax. — Each person who is engaged in the business of accepting wagers shall be liable for and shall pay the tax under this subchapter on all wagers placed with him. Each person who conducts any wagering pool or lottery shall be liable for and shall pay the tax under this subchapter on all wagers placed in such pool or lottery.” 68A Stat. 525.
  Section 4411 of the Code provides: “There shall be imposed a special tax of $50 per year to be paid by each person who is liable for tax under section 4401 or who is engar .. ■ mceiving wagers for or on behalf of any person so liable.” 68a rita 27.
  Section 4421 of the Code includes.in the definition of “wager" “any wager placed in a lottery conducted for profit” and includes in the definition of “lottery” “the numbers game, policy, and similar types of wagering.” 68A Stat. 528.
  Section 7201 of the Code provides: “Any person who willfully attempts in any manner to evade or defeat any tax imposed by this title or the payment thereof shall ... be guilty of a felony . . .” 68A Stat. 851.
  .18 U. S. C. §371 provides: “If xwo ormore persons conspire . . . to commit any offense against the United States, . . . and one or more of such persons do any act to effect the object of the conspiracy, each shall be fined ... or imprisoned . . . .” 62 Stat. 701.
  These were the links in the statutory chain under which the petitioners were indicted and convicted.
  Some of the items found when the headquarters of the operation was raided in 1957 were clearly indicative of the magnitude of the enterprise. Among the items found on that occasion were some 2,400 scratch pads of the type used in numbers operations, thousands of coin wrappers, a police alarm radio, with a secret code of police calls, two high-frequency radios, and six fictitious automobile registrations with license ta’gs. Petitioner Ingram was alleged to have stated in 1955 that the “business is down to about” $3,500 per day.
  Georgia Code (1953 Revision), § 26-6502.
  There was extensive evidence, for example, that participants in the enterprise used false license plates on their automobiles, took evasive routes to the “check-up headquarters” of ,the operation, used false names on occasion, and attempted to bribe local, law enforcement officers.
  See Note 1, supra.
  This section of the Code provides: “Any person required under this title to pay any . . . tax, . . . who willfully fails to pay such . . . tax, . . . shall ... be guilty of a misdemeanor . . . .” 68A Stat. 851.
  This section of the Code provides: “Each person required to pay a special tax under this subchapter shall register, with the official in charge of the internal revenue district— . . . .” 68A Stat. 527.
  This section, of the Code provides: “Any person who fails to register with the Secretary or his delegate as required by this title . . . shall be liable to a penalty of $50.” 68A Stat. 866.
  See “Developments in the Law — Criminal Conspiracy,” 72 Harv. L. Rev. 920, at 939, and authorities there cited.
  The Court’s decisions in Grunewald v. United States, 353 U. S. 391; Lutwak v. United States, 344 U. S. 604; and Krulewitch v. United States, 336 U. S. 440, do not, as petitioners appear to contend, prevent the jury from treating this subsidiary objective as an element of the conspiracy. Those cases hold only that the life of the conspiracy cannot be extended by evidence of concealment after the conspiracy’s criminal objectives have been fully accomplished. . . [A] vital distinction must be made between acts of concealment done in furtherance of the main criminal objectives of the conspiracy, and acts of concealment done after these central objectives have been attained, for the purpose only of covering up after the crime.’.’ Grunewald v. United States, supra, at 405.