ASHINGTON, Jan. 19 - A Supreme Court argument on Wednesday posed a civics question with practical implications: Is a political party's primary election basically the business of the party, or of the state?

Oklahoma was appealing a federal court decision that would have allowed political parties to open their nominating process to nonmembers.

Along with 23 other states, Oklahoma does not permit voters registered in one party to vote in another party's primary. Independent voters in Oklahoma may choose a party primary in which to vote, but those enrolled in a party may not cross party lines unless they "disaffiliate" from their party eight weeks before the election.

The federal appeals court in Denver, ruling last year on a challenge brought by Oklahoma's tiny Libertarian Party, held that the restriction violated the party's freedom of association under the First Amendment.

With only a few hundred members, the Oklahoma Libertarian Party wanted to broaden its appeal by opening its nominating process to members of other parties. But that strategy threatened to destabilize the political system, Oklahoma's assistant attorney general, Wellon B. Poe Jr., told the justices on Wednesday. "The state has an interest in a stable political system, which may be a two-party system," Mr. Poe said.

Oklahoma's argument, supported by eight other states as friends of the court, received a generally skeptical response. "So the state's interest here is in protecting the major parties from losing their members?" Justice Anthony M. Kennedy asked Mr. Poe.

Such an argument was "contrary to the thrust of our jurisprudence," Justice Kennedy added.

In a case from Connecticut in 1986, the court ruled that the state had to permit independents to vote in the Republican primary. In that case, the Republicans wanted to broaden their base, and sought more openness than the state allowed. Five years ago, the court confronted the opposite situation, a California law that imposed openness on political parties that did not want it. Once again, the parties prevailed against the state.

The court invalidated California's "blanket primary" system, in which all voters, regardless of party affiliation, received a single primary ballot from which they could select nominees of any party - a Democrat for governor and a Republican for the State Senate, for example.

That system, which had been adopted by a voter referendum in 1996, was challenged by the state's Democratic and Republican Parties along with two smaller parties. The parties argued that they did not want to lose control of their nominating process. Writing for the court, Justice Antonin Scalia said the provision violated the parties' important "right to exclude" and to limit its internal selection process to its own membership.

The Oklahoma case, Clingman v. Beaver, No. 04-37, presents the other side of that coin, said the Libertarian Party's lawyer, James C. Linger, who argued that a party should have the right to include others as well as exclude them.

"The integrity of a political party should be defined by a political party and not by the state," Mr. Linger told the justices.

In Oklahoma's appeal, the state is arguing that its restriction is necessary to prevent parties from raiding one another's membership. Mr. Linger said the state's concern was misplaced.

"We should not be worrying about protecting major parties from the competition for ideas," he said.

Justice Scalia, however, appeared to find merit in the state's position. The reason for having party designations in the first place, he observed, was to give voters an idea of what the candidates stand for.

"If it's running as a party, it should run candidates who share those views," he said. "That seems to me to make a lot of sense."

Unlike the California case, the major parties in Oklahoma did not become involved in the challenge to the state's primary law. They neither participated in the lawsuit nor filed briefs at the Supreme Court stage. Why should the state protect the parties' interests if the parties were not motivated to speak for themselves, Justice Ruth Bader Ginsburg asked Mr. Poe, the state's lawyer.

"The state has to protect its interest whether the parties are involved or not," he replied.

Justice Scalia then provided another explanation.

"I suppose if I were the Democratic or Republican Party chairman, I wouldn't want to alienate my members by depriving them of the freedom of voting in the Libertarian primary," he said. "It makes you look parsimonious. They are, after all, politicians, aren't they?"