The winning plaintiffs who successfully challenged bans on same-sex marriage in Virginia, Oklahoma and Utah all are asking the Supreme Court to take up the issue this term, saying their victories are incomplete unless same-sex couples everywhere are treated the same.

It is somewhat unusual for the winning side to ask the Supreme Court to review a decision. But the justices have prevented marriages from taking place while they contemplate taking up the issue, and the challengers say the uncertainty needs to end.

And, not surprisingly, each would like to be the case that the court accepts in order to decide a landmark constitutional issue.

The Virginia couples say that even though they won at the U.S. Court of Appeals for the 4th Circuit, they “still face the intolerable prospect that their marriages will not be recognized should they travel or relocate” to another state, according to documents filed by their attorneys, Theodore Olson and David Boies.

“Given the critical importance of this issue to plaintiffs and to hundreds of thousands of other gay men and lesbians across the country — as well as to their children and extended families — this court’s review is acutely needed.”

Same-sex marriage status in the U.S., state-by-state

After the justices last week issued a stay to keep same-sex marriages in Virginia from commencing, lawyers representing a class of same-sex couples in the state asked the Supreme Court to settle the issue.

“Virginia’s same-sex couples apparently will be unable to benefit from the Fourth Circuit’s mandate vindicating their freedom to marry unless and until this court has addressed the merits of the constitutional question presented here,” said a brief filed by Washington lawyer Paul Smith on behalf of the American Civil Liberties Union.

Winning couples in Oklahoma also are asking the court to step in now. “The time has come for this court to decide whether state laws denying same-sex couples the right to marry should be discarded into the . . . ash heap of history,” says a filing on their behalf from Stanford Law School’s Jeffrey L. Fisher, who is new to their legal team.

Utah plaintiffs have said they would accede to the state’s plea that the Supreme Court accept its appeal of a decision from the U.S. Court of Appeals for the 10th Circuit. The same three-judge panel of that court found the bans in Utah and Oklahoma were unconstitutional.

The filings are part of an effort to have the Supreme Court decide sooner rather than later whether the Constitution requires the fundamental right to marriage be extended to same-sex couples.

By filing the documents Wednesday, the plaintiffs believe the cases will be ready for the justices to consider when they assemble Sept. 29 for their first private conference of the fall. The court is under no obligation to act .

But Fisher said the parties want the court to have as much time as it needs to consider the requests. If the court decides to accept one or more of the cases this fall, oral arguments would probably come early next year, with a decision by the time the court’s term ends in June.

The rapid movement of the issue follows the Supreme Court’s action in June 2013. The court narrowly voided part of the Defense of Marriage Act, which defined marriage for federal purposes as only between a man and a woman.

The court did not decide the larger question of whether states may impose bans on same-sex marriage. But since then, nearly two dozen federal courts have used the reasoning of the court’s decision to rule that the bans are unconstitutional.

The chance to argue a historic case before the high court has attracted a number of high-profile lawyers.

Olson and Boies joined the Virginia case after bringing a challenge to California’s ban on gay marriage to the Supreme Court in 2012. But the justices said procedural difficulties prevented them from ruling on the constitutionality of state bans; it dismissed the case in a way that allowed marriages to resume in the state, but without setting a precedent for others.

Smith, joining forces with the ACLU in its challenge of the Virginia ban, argued the case in which the justices struck down bans on homosexual conduct. Fisher argues frequently before the court, and Neal Katyal, a former acting solicitor general in the Obama administration, joined the Utah effort.

Virginia’s case has the most unusual procedural background. Attorney General Mark Herring (D) decided after taking office that the law was unconstitutional. He refused to defend it, and joined challengers in asking it be declared unconstitutional.

The law is being defended by two circuit clerks. In Utah and Oklahoma, state officials are united in trying to protect their laws.

But Olson said the case made an attractive vehicle for the court, making a reference to Loving v. Virginia, in which the Supreme Court in 1967 struck down a state ban on inter-racial marriage.

“It is time thousands of gay and lesbian couples across America are extended that same promise of equality and freedom that the Supreme Court granted to the Lovings,” Olson said in a statement.