opinion: Mr. Chief Justice Burger
  delivered the opinion of the Court.
  A three-judge District Court in the Northern District of Illinois upheld the constitutionality of a provision of the Social Security Act which provides that certain illegitimate children, who cannot qualify for benefits under any other provision of the Act, may obtain benefits if, but only if, the disabled wage-earner parent is shown to have contributed to the child’s support or to have lived with him prior to the parent’s disability. The District Court held that the statute’s classification is rationally related to the legitimate governmental interest of avoiding spurious claims. Jimenez v. Richardson, 353 F. Supp. 1356, 1361 (1973). We noted probable jurisdiction. 414 U.S. 1061.
  The relevant facts are not in dispute. Ramon Jimenez, a wage earner covered under the Social Security Act, became disabled in April 1963, and became entitled to disability benefits in October 1963. Some years prior to that time, the claimant separated from his wife and began living with Elizabeth Herñandez, whom he never married. Three children were born to them, Magdalena, born August 13, 1963, Eugenio, born January 18, 1965, and Alicia, born February 24, 1968. These children have lived in Illinois with claimant all their lives; he has formally acknowledged them to be his children, has supported and cared for them since their birth, and has been their sole caretaker since their mother left the household late in 1968. Since the parents never married, these children are classified as illegitimate under Illinois law and are unable to inherit from their father because they are nonlegitimated illegitimate children. Ill. Ann. Stat., c. 3, § 12 (Supp. 1974).
  On August 21,1968, Ramon Jimenez, as the father, filed an application for child’s insurance benefits on behalf of these three children. Magdalena was found to be entitled to child’s insurance benefits under the Social Security Act, and no issue is presented with respect to her claim. The claims of appellants, Eugenio and Alicia, were denied, however, on the ground that they did not meet the requirements of 42 U. S. C. § 416 (h) (3), since neither child’s paternity had been acknowledged or affirmed through evidence of domicile and support before the onset of their father’s disability. In all other respects Eugenio and Alicia are eligible to receive child’s insurance benefits, and their applications were denied solely because they are proscribed illegitimate children who were not dependent on Jimenez at the time of the onset of his disability.
  Appellants urge that the contested Social Security provision is based upon the so-called “suspect classification” of illegitimacy. Like race and national origin, they argue, illegitimacy is a characteristic determined solely by the accident of birth; it is a condition beyond the control of the children, and it is a status that subjects the children to a stigma of inferiority and a badge of opprobrium. We need not reach appellants’ argument, however, because in the context of this case it is enough that we note, as we did in Weber v. Aetna Casualty & Surety Co., 406 U.S. 164 (1972):
  “The status of illegitimacy has expressed through the ages society’s condemnation of irresponsible liaisons beyond the bonds of marriage. But visiting this condemnation on the head of an infant is illogical and unjust. Moreover, imposing disabilities on the illegitimate child is contrary to the basic concept of our system that legal burdens should bear some relationship to individual responsibility or wrongdoing. Obviously, no child is responsible for his birth and penalizing the illegitimate child is an ineffectual — as well as an unjust — way of deterring the parent. Courts are powerless to prevent the social opprobrium suffered by these hapless children, but the Equal Protection Clause does enable us to strike down discriminatory laws relating to status of birth where . . . the classification is justified by no legitimate state interest, compelling or otherwise.” Id., at 175-176.
  Conversely, the Secretary urges us to uphold this statutory scheme on the ground that the case is controlled by the Court’s recent ruling in Dandridge v. Williams, 397 U. S. 471 (1970), where we noted:
  “In the area of economics and social welfare, a State does not violate the Equal Protection Clause merely because the classifications made by its laws are imperfect. If the classification has some 'reasonable basis,’ it does not offend the Constitution simply because the classification ‘is not made with mathematical nicety or because in practice it results in some inequality.’ Lindsley v. Natural Carbonic Gas Co., 220 U. S. 61, 78. ‘The problems of government are practical ones and may justify, if they do not require, rough accommodations — illogical, it may be, and unscientific.' Metropolis Theatre Co. v. City of Chicago, 228 U. S. 61, 69-70. 'A statutory discrimination will not be set aside if any state of facts reasonably may be conceived to justify it.’ McGowan v. Maryland, 366 U. S. 420, 426.” Id., at 485.
  However, Dandridge involved an equal protection attack upon Maryland’s Aid to Families with Dependent Children program which provided aid in accordance with the family’s standard of need, but limited the maximum grant to $250 per family, regardless of size, thereby reducing the per capita allowance for children of large families. We noted that the AFDC welfare program is a “ ‘scheme of cooperative federalism’ ” and that the “starting point of the statutory analysis must be a recognition that the federal law gives each State great latitude in dispensing its available funds.” Id., at 478. This special deference to Maryland’s statutory approach was necessary because, “[g]iven Maryland’s finite resources, its choice is either to support some families adequately and others less adequately, or not to give sufficient support to any family.” Id., at 479. Here, by contrast, there is no evidence supporting the contention that to allow illegit-imates in the classification of appellants to receive benefits would significantly impair the federal Social Security trust fund and necessitate a reduction in the scope of persons benefited by the Act. On the contrary, the Secretary has persistently maintained that the purpose of the contested statutory scheme is to provide support for dependents of a wage earner who has lost his earning power, and that the provisions excluding some afterborn illegitimates from recovery are designed only to prevent spurious claims and ensure that only those actually entitled to benefit receive payments. Accepting this view of the relevant provisions of the Act, we cannot conclude that the purpose of the statutory exclusion of some afterborn illegitimates is to achieve a necessary allocation of finite resources and, to that extent, Dandridge is distinguishable and not controlling.
  As we have noted, the primary purpose of the contested Social Security scheme is to provide support for dependents of a disabled wage earner. The Secretary maintains that the Act denies benefits to afterborn illegit-imates who cannot inherit or whose illegitimacy is not solely because of a formal, non obvious defect in their parents’ wedding ceremony, or who are not legitimated, because it is “likely” that these illegitimates, as a class, will not possess the requisite economic dependency on the wage earner which would entitle them to recovery under the Act and because eligibility for such benefits to those illegitimates would open the door to spurious claims. Under this view the Act’s purpose would be to replace only that support enjoyed prior to the onset of disability; no child would be eligible to receive benefits unless the child had experienced actual support from the wage earner prior to the disability, and no child born after the onset of the wage earner’s disability would be allowed to recover. We do not read the statute as supporting that view of its purpose. Under the statute it is clear that illegitimate children born after the wage earner becomes disabled qualify for benefits if state law permits them to inherit from the wage earner, § 416 (h) (2) (A); or if their illegitimacy results solely from formal, nonobvious defects in their parents’ ceremonial marriage, § 416 (h) (2) (B); or if they are legitimated in accordance with state law, § 402 (d)(3)(A). Similarly, legitimate children born after their wage-earning parent has become disabled and legitimate children born before the onset of disability are entitled to benefits regardless of whether they were living with or being supported by the disabled parent at the onset of the disability, §§ 402 (d) (1) and (3).
  In each of the examples just mentioned, the child is by statute “deemed dependent” upon the parent by virtue of his status and no dependency or paternity need be shown for the child to qualify for benefits. However, nonlegitimated illegitimates in appellants’ position, who cannot inherit under state law and whose illegitimacy does not derive solely from a defect in their parents’ wedding ceremony, are denied a parallel right to the dependency presumption under the Act. Their dilemma is compounded by the fact that the statute denies them any opportunity to prove dependency in order to establish their “claim” to support and, hence, their right to eligibility. § 416 (h) (3) (B). The Secretary maintains that this absolute bar to disability benefits is necessary to prevent spurious claims because “[t]o the unscrupulous person, all that prevents him from realizing . . . gain is the mere formality of a spurious acknowledgment of paternity or a collusive paternity suit with the mother of an illegitimate child who is herself desirous or in need of the additional cash.” Jimenez v. Richardson, 353 F. Supp., at 1361.
  From what has been outlined it emerges that afterborn illegitimate children are divided into two subclassifica-tions under this statute. One subclass is made up of those (a) who can inherit under state intestacy laws, or (b) who are legitimated under state law, or (c) who are illegitimate only because of some formal defect in their parents’ ceremonial marriage. These children are deemed entitled to receive benefits under the Act without any showing that they are in fact dependent upon their disabled parent. The second subclassification of afterborn illegitimate children includes those who are conclusively denied benefits because they do not fall within one of the foregoing categories and are not entitled to receive insurance benefits under any other provision of the Act.
  We recognize that the prevention of spurious claims is a legitimate governmental interest and that dependency of illegitimates in appellants’ subclass, as defined under the federal statute, has not been legally established even though, as here, paternity has been acknowledged. As we have noted, the Secretary maintains that the possibility that evidence of parentage or support may be fabricated is greater when the child is not born until after the wage earner has become entitled to benefits. It does not follow, however, that the blanket and conclusive exclusion of appellants’ subclass of illegitimates is reasonably related to the prevention of spurious claims. Assuming that the appellants are in fact dependent on the claimant, it would not serve the purposes of the Act to conclusively deny them an opportunity to establish their dependency and their right to insurance benefits, and it would discriminate between the two subclasses of afterborn illegit-imates without any basis for the distinction since the potential for spurious claims is exactly the same as to both subclasses.
  The Secretary does not contend that it is necessarily or universally true that all illegitimates in appellants’ subclass would be unable to establish their dependency and eligibility under the Act if the statute gave them an opportunity to do so. Nor does he suggest a basis for the assumption that all illegitimates who are statutorily deemed entitled to benefits under the Act are in fact dependent upon their disabled parent. Indeed, as we have noted, those illegitimates statutorily deemed dependent are entitled to benefits regardless of whether they were living in, or had ever lived in, a dependent family setting with their disabled parent. Even if children might rationally be classified on the basis of whether they are dependent upon their disabled parent, the Act’s definition of these two subclasses of illegitimates is “over-inclusive” in that it benefits some children who are legitimated, or entitled to inherit, or illegitimate solely because of a defect in the marriage of their parents, but who are not dependent on their disabled parent. Conversely, the Act is “underinclusive” in that it conclusively excludes some illegitimates in appellants’ subclass who are, in fact, dependent upon their disabled parent. Thus, for all that is shown in this record, the two subclasses of illegitimates stand on equal footing, and the potential for spurious claims is the same as to both; hence to conclusively deny one subclass benefits presumptively available to the other denies the former the equal protection of the laws guaranteed by the due process provision of the Fifth Amendment. Schneider v. Rusk, 377 U. S. 163, 168 (1964); Bolling v. Sharpe, 347 U. S. 497, 499 (1954).
  In the District Court the Secretary, relying on the validity of the statutory exclusion, did not undertake to challenge the assertion that appellants are the children of the claimant, that they lived with the claimant all their lives, that he has formally acknowledged them to be his children, and that he has supported and cared for them since their birth. Accordingly, the judgment is vacated and the case is remanded to provide appellants an opportunity, consistent with this opinion, to establish their claim to eligibility as “children” of the claimant under the Social Security Act.
  Vacated and remanded.
  42 U. S. C. §416 (h)(3).
  The contested Social Security scheme provides, in essence, that legitimate or legitimated children (42 U. S. C. § 402 (d) (3)), illegitimate children who can inherit their parent’s personal property under the intestacy laws of the State of the insured’s domicile (42 U. S. C. § 416 (h) (2) (A)), and those children who cannot inherit only because their parents’ ceremonial marriage was invalid for nonobvious defects (42 U. S. C. § 416 (h) (2) (B)), are entitled to receive benefits without any further showing of parental support. However, illegitimate children such as Eugenio and Alicia who were not living with or being supported by the applicant at the time the claimant’s period of disabilhy began, and who do not fall into one of the foregoing categories, are not entitled to receive any benefits. 42 U. S. C. § 416 (b)(3).
  See House-Senate Conference Committee Report on 1965 Amendments to Social Security Act, 111 Cong. Rec. 18387 (1965); Report of the U. S. Advisory Council on Social Security, the Status of the Social Security Program and Recommendations for its Improvement 67 (1965).