WASHINGTON -- Groucho Marx once said he wouldn't want to belong to a club that would have him as a member, but the Libertarian Party of Oklahoma wants Democrats and Republicans who would never consider becoming Libertarians to be able to vote in its primary elections. Yesterday, the party asked the U.S. Supreme Court to free it from a state law prohibiting such crossover voting.

But lawyers for the state told the justices that the prohibition is justified by the need to ensure that candidates are faithful to the precepts of the parties that nominate them.

Several justices seemed to agree. Justice Antonin Scalia said the open-door policy favored by the Libertarians meant that "we don't have any policies; we just want to nominate someone." He said such a policy "destroys the whole purpose of letting people run under a party label."

James C. Linger, representing the Libertarians, responded: "The integrity of a political party should be determined by the party, and not by the state." He suggested that a decision in favor of the Libertarians would be a natural extension of a 1986 ruling in which the court held that Connecticut couldn't prevent the Republican Party from allowing independents to vote in the GOP primary.

In Oklahoma, political parties are likewise free to invite independents to take part in their primaries, but they may not put out the welcome mat for voters registered in another party. Without that ban, the justices were told, one party could "poach" the voters of a rival party, making the results in both primaries less reflective of the will of loyal party members.

Gene C. Schaerr, one of two lawyers who defended Oklahoma's law, said poaching was particularly a problem if a popular politician suddenly changed parties, tempting his admirers to follow him into another party's primary.

But several justices questioned the "poaching" theory. Justice David H. Souter wondered whether a Democratic or Republican voter disaffected enough to vote in another party's primary wouldn't simply stay home on Primary Election Day if he didn't have that option.

The justices seemed divided over the constitutional issue in the case -- whether the law infringes Oklahomans' First Amendment right to political association.

Justice Sandra Day O'Connor noted that the deadline for voter registration came so early -- eight weeks before the election -- that voters intrigued by a third party added to the ballot after that couldn't respond by changing registration in order to participate in that party's primary. "It gives them a very impossibly short window [of opportunity]," she said. "Isn't that kind of burdensome?"

But Scalia suggested that voters who are "ashamed of the L word" could keep their options by registering independent and then voting in the Libertarian contest on Primary Election Day.

Several justices worried that a ruling in favor of the Libertarians would mean that the Democratic and Republican parties also could hold open primaries. "I don't see how you could have a constitutional rule that allows you to drain voters from other parties, but not [give the same power to] the Democrats and the Republicans," Justice Stephen Breyer told Linger.

Linger suggested that the justices could rule narrowly for the Libertarians because, as a small party, they were especially burdened by early registration deadlines and other election rules.

Only two states -- Alaska and Utah -- have so-called "party-option open primaries" of the kind that the Libertarians want to hold in Oklahoma.

Twenty-four other states have open primaries, in which any registered voter can participate, and the remaining 24 states have either closed primaries (such as Pennsylvania's) limited to registered party members or "semi-closed" primaries, in which party members and independents can vote.