The third and final debate between President Bush and Senator Kerry has been thrown into doubt after a state judge in Arizona ordered a hearing on whether the event, scheduled for Wednesday, should be halted because the Libertarian Party’s nominee for president has not been invited.

Judge F. Pendleton Gaines III instructed the debate’s hosts, Arizona State University and the Commission on Presidential Debates, to appear in his courtroom in Phoenix tomorrow to respond to a lawsuit filed last week by the Libertarians.

“I’m happy so far with the way things are going,” an attorney for the Libertarian Party, David Euchner, said in an interview yesterday. “He did not have to sign that order. The fact that he did is a good sign.”

The suit argues that the university is illegally donating state resources to the Republican and Democratic Parties by serving as host for a debate that showcases Messrs. Bush and Kerry but excludes their Libertarian counterpart, Michael Badnarik, who is on the ballot in Arizona and 47 other states.

“They can’t have debates that make public expenditures for private benefit,” Mr. Euchner said. “A.S.U. is spending its money in violation of the state constitution.”

A spokeswoman for the university, Nancy Neff, said she was unaware of the hearing tomorrow. “If that’s the judge’s order, then we’ll be there for sure,” Ms. Neff said.

While the university is constructing a massive press filing center and has incurred large expenses for security, Ms. Neff insisted the debate will take place at no cost to taxpayers.

“We are not spending public money on the debate. We have underwritten it using private donations, in-kind gifts, and private foundation funds,” the university spokeswoman said. “The price we’ve been working with is $2.5 million, and that’s what we’ve been trying to raise,” Ms. Neff said.

Major sponsors for the third debate include a heavy equipment maker, Caterpillar Inc.; a local utility company, APS, and an Indian tribal group that owns two casinos near Scottsdale, the Salt River Pima-Maricopa Indian Community.

Ms. Neff acknowledged, however, that the university has yet to raise all the funds required for the event, which is scheduled to take place at an auditorium on the school’s Tempe campus, just east of Phoenix. “We’re still raising money even as we work on it,” she said, adding that at the last tally about $2.3 million had been pledged.

Mr. Euchner said the university’s claim that no public money is involved is laughable. “The fact they’ve got their hat in hand helps us,” he said. “The evidence is pretty clear that if there’s a shortfall here that A.S.U. is holding the bag. They made, essentially, an interest free loan.”

Mr. Euchner said the state’s involvement in the debate is part of what many Libertarians see as a pattern of improper use of government funds to promote the two major parties. “Taxpayers foot the bill for the Democratic and Republican national conventions,” he complained. “Anything they can get the taxpayers to pay for that way, they do it.”

Several legal experts said the Libertarians face an uphill battle in attempting to use the so-called gift clause of the Arizona Constitution to block Wednesday’s debate.

“It doesn’t strike me as a very strong ground,” an author of a book on the Arizona Constitution, Toni McClory, said. “It’s not a violation of the gift clause if the state is getting something of real value.” While state universities have been hosts to presidential debates in the past, Arizona State is the only one to do so this year.

Ms. McClory, who teaches at a community college near Phoenix, said the publicity surrounding the debate might be considered a substantial benefit to the university. “It’s giving the university a great deal of public exposure,” she said.

A law professor at the University of Arizona, Robert Glennon, said the court dispute is likely to turn on whether Arizona State is seen as discriminating against the Libertarians. He said offering the Libertarians the use of a similar facility on campus would probably be enough to fulfill the state’s obligations.

“So long as the state has a nondiscriminatory policy, the fact that one particular party or one religion uses it is of no consequence,” Mr. Glennon said. The professor noted that the requirements to bring a case for abuse of taxpayer funds are often lower in state courts than in the federal system, but he said he was surprised that the judge granted the Libertarians a hearing.

Judge Gaines was appointed to the bench in 1999 by Gov. Jane Hull, a Republican. In his show-cause order issued Friday morning, the judge also required that the university and the debate commission be served with the lawsuit by Friday afternoon. An attorney for the university accepted service, but security guards at the commission’s headquarters in Washington ordered process-servers to leave the building, Mr. Euchner said.

Indeed, Mr. Badnarik and the Green Party nominee, David Cobb, were arrested Friday night after they crossed a police line at the presidential debate in St. Louis. Mr. Badnarik said he was trying to serve the lawsuit on a representative of the debate commission. The two candidates were released after being given tickets for trespassing and refusing a reasonable order from a policeman.

The commission, which is a nonprofit corporation, has insisted that it applies nonpartisan criteria to determine who is invited to the debates. The rules require that candidates have at least 15% support in national polls to qualify. None of the third-party candidates this year has met that hurdle.

Critics of the debate commission assert that it is little more than a front for the major parties. They note that the Democrats and the GOP issued a joint press release announcing the creation of the “bipartisan” commission and describing its purpose as facilitating debates between their “respective nominees.” More recently, the commission has described itself as “nonpartisan,” although its adherence to that standard remains in question.

Last month, a spokesman for the debate commission told the Sun that the panel could not comply with a provision in the agreement worked out between the Bush and Kerry campaigns that dictated the makeup of the audience for Friday’s town meeting debate be one-half “soft” supporters of Mr. Bush and one-half “soft” supporters of Mr. Kerry. “We can’t use soft Bush and soft Kerry supporters because we are a nonpartisan group, not a bipartisan group,” said the commission spokesman, who asked not to be named. “We have said we’d use undecided voters.”

In an interview with CNN last week, the editor in chief of Gallup, Frank Newport, said that more than 90% of those in the audience for Friday’s debate had stated a “soft” preference for either Mr. Bush or Mr. Kerry. Mr. Newport did not indicate whether supporters of the independent candidate Ralph Nader or of Mr. Badnarik were considered for the audience.

In August, a federal judge in Washington sharply criticized the Federal Election Commission for ignoring evidence of bias on the part of the debate commission. Judge Henry Kennedy Jr. noted that in 2000 the debate commission gave security guards “facebooks” with pictures of third-party candidates and instructed the guards to prevent those in the photos from entering the debate venues, even with valid audience tickets. “The exclusion policy appears partisan on its face,” Judge Kennedy wrote.

In a national poll taken in September, 57% of likely voters favored including presidential candidates other than the president and the Massachusetts senator in the debates. The survey, conducted by Zogby International, found 57% of likely voters in favor of adding Mr. Nader, and 44% in favor of including Mr. Badnarik.