JACKSONVILLE, Fla. — A federal appeals court is struggling with the case of a former Florida college professor who admitted to aiding Palestinian Islamic Jihad but later insisted that his plea deal precluded the government from calling him before a grand jury investigating Islamic charities in Virginia. The 11th Circuit Court of Appeals heard oral arguments for 45 minutes here yesterday about the dispute’s circuitous journey through four federal courts, resulting in the professor, Sami Al-Arian, spending nine months in jail, so far, for refusing to testify before the Alexandria, Va.-based grand jury.

“This is such a mess,” one member of the three-judge appeals panel, Rosemary Barkett, declared.

“It is a mess,” the prosecutor arguing for the government, Karin Hoppmann, replied. “It’s a Gordian knot,” she added in a later exchange.

A vexing legal problem in the case stems from the fact that the Virginia-based judge in charge of the grand jury, Gerald Lee, referred the dispute about the meaning of Al-Arian’s plea deal to a Tampa-based jurist, James Moody Jr., who accepted Al-Arian’s plea and oversaw an earlier trial at which the Palestinian Arab activist was acquitted on some charges. A federal prosecutor in Virginia backed the referral, but the government later took the position that referring such legal questions to another jurisdiction is illegal and unconstitutional.

Ms. Hoppmann, who is based in Tampa, said yesterday that the Virginia-based prosecutor, Gordon Kromberg, made “a mistake” when he agreed that the plea issue should be settled in Florida.

A lawyer for Al-Arian, Jack Fernandez of Zuckerman Spaeder, complained that it was unfair to fault Al-Arian for seeking relief in Florida when Judge Lee ordered him to go there and the government concurred. “We’re being whipsawed. This is checkmate,” Mr. Fernandez said.

Judge Barkett expressed some sympathy with that view, wondering aloud why Judge Lee did not wait for Al-Arian’s 11th Circuit appeal to be concluded before jailing him for contempt.

The government and Al-Arian are also at loggerheads over the meaning of his plea deal. He and his lawyers contend that they negotiated with prosecutors to drop language about cooperation because he was bitter about his treatment and insistent that he would not aid the government in any way. Prosecutors acknowledge they dropped the language but they say nothing in the agreement gave Al-Arian a license to defy subpoenas. “I don’t see how you can manufacture some promise that he wouldn’t be called before a grand jury…that wasn’t in the plea agreement,” a federal district court judge from Brooklyn handling the appeal as part of a rotating pool of visiting jurists, Edward Korman, said.

“You asked the district court below to enforce an agreement that doesn’t have in it the provision that you want to enforce?” Judge Barkett asked Al-Arian’s lawyer. “A plea agreement is not just like any contract,” Mr. Fernandez said. Courts should not be complicit in a situation where the government “inveigles a plea” with some inducement outside the written agreement, he said.

In 1992, the 4th Circuit Court of Appeals, which includes Virginia, ruled that prosecutors could be held to a no-testimony promise not recorded in a formal plea agreement. However, the third judge assigned to Al-Arian’s appeal, Stanley Birch Jr., said he saw little merit in that decision. “To me, it’s contrary to logic,” he said. The most contentious exchange yesterday came as Ms. Hoppmann dodged a question about whether the government made any promises to Al-Arian during plea talks. “I was not there. I do not know,” she said.

Apparently exasperated, Judge Barkett raised her voice, asking the government attorney if “as an officer of the court” she was saying she had no information at all about what transpired. Ms. Hoppmann eventually quoted another prosecutor’s brief account of the negotiations at another court hearing, but never said explicitly whether she was aware of other details about the talks.

While no judge took a clear stance on the case yesterday, Judges Birch and Barkett seemed inclined to void Judge Moody’s decision for lack of jurisdiction. Judge Korman dismissed that issue as quibbling over “a geographic line.” “That’s a geographic line Congress has set down,” Ms. Hoppmann replied.

It’s not clear whether Al-Arian would benefit from a ruling vacating Judge Moody’s decision. There are indications that, even without Judge Moody’s guidance, Judge Lee might reject Al-Arian’s view of his plea deal. In addition, Al-Arian, who has been in jail since 2003, has about four more months to serve on the nearly five years he was sentenced to following his guilty plea. The clock on that sentence stopped running when Al-Arian was jailed for contempt.

Under federal law, Al-Arian cannot spend more than 18 months in jail for civil contempt. However, prosecutors could charge him with criminal contempt, which can result in an additional prison term of indeterminate length. Al-Arian has agreed to be deported upon his release.

Shortly before the arguments were to take place yesterday, court personnel indicated that the public would be excluded, although no motion to close the courtroom was filed. As Al-Arian’s case neared, extra marshals appeared.

During a break between earlier cases, this reporter gave a note to a court clerk objecting to any closure. When the Al-Arian case was called, Judge Birch said the courtroom would be cleared of spectators so the judges could hear from the government and Al-Arian’s attorney about whether the arguments should take place publicly. As those in the gallery were being ushered out, this reporter asked aloud if a member of the press could present arguments opposing any secret session. Judge Birch declined, saying the court could “handle it.”

Within a few minutes, the marshals reopened the courtroom. “It must have been your brilliant argument,” Judge Barkett said to this reporter, facetiously.

“Do you want to argue your way out of it?” Judge Birch asked with a chuckle.

“I’m going to keep my mouth shut,” the reporter replied.

While the appeal touches on a grand jury matter, which is usually secret, the Virginia panel’s focus and Al-Arian’s status as a so-called recalcitrant witness there have long been public in court files.

Judge Birch was appointed by President George H.W. Bush, Judge Barkett by President Clinton, and Judge Korman by President Reagan.