BOSTON—Regardless of who wins today's special election in Massachusetts, it could be several days before the state's next senator is seated on Capitol Hill. If Tuesday's balloting proves razor thin—and is marked by irregularities—it could take weeks.

Here's an overview of the issues that may come up in the days ahead.

Who's current filling the Massachusetts seat?

Sen. Paul Kirk, a former aide to the late Sen. Edward Kennedy and longtime Kennedy family friend, was appointed to fill the seat after the state legislature passed a bill allowing Massachusetts Gov. Deval Patrick to name an interim replacement.

Mr. Kirk, 72 years old, once chaired the Democratic National Committee. He took the oath of office Sept. 25, one day after he was appointed. He created a stir recently by saying he would "absolutely" vote to pass a health-care bill before a replacement takes office.

When will the new U.S. senator be seated?

Senate rules require any prospective senator to present to the Secretary of the Senate papers certifying the election was fairly conducted, that there are no challenges pending and that the individual meets the basic qualifications for office. Once those papers are deemed in order, the candidate is then declared a senator-elect, which comes with privileges of the floor and office space. The senator-elect would be sworn into office by the vice president, usually in a matter of days.

Under Massachusetts law, state officials cannot formally certify an election until ten days after Election Day. The delay allows local officials to count late-arriving absentee and military ballots; after that local officials have another five days to transmit final results to the state.

If Tuesday's preliminary results show a clear victor, the Secretary of the Commonwealth, William Galvin, could send a letter to the Senate essentially declaring a winner. "But the question is, what would the Senate do?" said Brian McNiff, Mr. Galvin's spokesman.

A few years ago, Mr. Galvin sent such a letter on behalf of Democrat Nicki Tsongas, after she won a decisive victory in a special election for an open House seat. Ms. Tsongas was sworn into office two days after her election.

Senate Minority Leader Mitch McConnell (R., Ky.) has said whoever wins Tuesday "should be sworn in promptly." Jim Manley, a spokesman for Senate Majority Leader Harry Reid (D., Nev.), said the Senate has different rules than the House, and they must be followed.

"When there is a certified winner in Massachusetts, the Senate has received appropriate papers, and the Vice President is available, the successor to Senators Kennedy and Kirk will be sworn in," he said.

Can the ballots be counted again?

Under state law, a candidate can request a recount if the margin of victory is less than one half of one percent of the total votes cast. The party requesting the recount must gather 1,000 signatures before the Secretary of the Commonwealth would start the recount.

What if there are irregularities?

If the margin of victory is close, irregularities could spur a legal challenge, especially if they are considered widespread enough to change the outcome. Such irregularities could include allowing individuals with improper registration to vote or counting absentee ballots mailed after Election Day.

"What the lawyers will be looking for – on the losing side—are anything they could hang their hat on," said Guy-Uriel Charles, an election law expert at Duke University. "They are going to be scouring for anything."

—Louise Radnofsky contributed to this article.

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