When the Supreme Court hears arguments today about the rights of suspects held at the Guantanamo Bay military prison, the role of the courts in the fight against terrorism will be as much an issue as the fate of the prisoners.

The president and Congress have already made their opinions clear: The courts may not "hear or consider" challenges from foreigners held as enemy combatants at the U.S. facility in Cuba.

But in what some scholars say is a critical separation-of-powers case, the nine justices will have the final word on whether such a court-stripping prohibition is constitutional, and on how deferential the judicial branch should be in the prosecution of a war unlike any the country has ever faced.

The court has been critical of Bush administration policies over the past three years, but "this case is probably more important than the other ones because it's a direct conflict between the political branches that have traditionally run wars and the courts," said John Yoo, a former Justice Department official who helped design the Bush administration's legal strategies for the terrorism fight.

Yoo denounced the court's involvement and said that it has never received such an unequivocal message that the "joint wishes of the president and Congress" are to "push the courts out" of the process.

Attorneys for the detainees and a host of international and domestic interest groups supporting them say that is precisely when the courts are most needed.

The libertarian Cato Institute, in a brief filed by lawyer Timothy Lynch, said it is "imperative that this Court eschew a deferential posture and stand, in words of James Madison, as an 'impenetrable bulwark against every assumption of power in the Legislative or Executive.' "

Two cases, Boumediene v. Bush and Al Odah v. United States, have been consolidated into one and brought on behalf of 37 foreigners who remain among the approximately 300 detainees at Guantanamo Bay. All were captured on foreign soil and have been designated enemy combatants. They proclaim their innocence and for years have asked federal courts for a writ of habeas corpus, the ancient right allowing prisoners to challenge their detentions.

Some have been imprisoned since soon after the attacks of Sept. 11, 2001, and while they have won at the Supreme Court before, none has had a full hearing before a federal judge.

The court has confronted the issue before, ruling in 2004 in Rasul v. Bush that federal habeas corpus statutes extended to Guantanamo Bay detainees because of the unique control that the U.S. government has over the land.

The Republican-led Congress responded by changing the law, and after another adverse court ruling and at the urging of the Bush administration, it passed the Military Commissions Act in October 2006. The legislation endorsed a military system for designating detainees as enemy combatants and for trying those charged with crimes, and it strictly limited judicial oversight.

"The detainees now enjoy greater procedural protections and statutory rights to challenge their wartime detentions than any other captured enemy combatants in the history of war," Solicitor General Paul D. Clement said in his brief to the court. "Yet they claim an entitlement to more."

Specifically, attorneys contend that Guantanamo Bay detainees have a constitutional guarantee of habeas, a right that Congress may suspend only in times of "rebellion or invasion."

The government disputes that, but says that even if it were so, previous court rulings allow an adequate substitute for habeas proceedings.

But detainees who appear before the military Combatant Status Review Tribunals, which determine whether they can be held indefinitely as enemy combatants, have fewer rights than they would in habeas proceedings. They are not represented by counsel, do not have access to all evidence used against them and cannot prevail on a judge to release them if the case against them is not made.

"Habeas is a judicial remedy," former solicitor general Seth P. Waxman, who will argue for the detainees, said in a brief. "It cannot be replaced by a process that (like the CSRT) is ultimately controlled by the jailer."

The position is supported by a long list of organizations that have filed briefs with the court on behalf of the detainees: Israeli leaders, who say that terrorism suspects in their country receive a detention hearing within 14 days; a group of 383 European parliamentarians; former U.S. diplomats; law professors; retired military leaders; and even Sen. Arlen Specter (R-Pa.), who voted for the Military Commissions Act and said at the time that the court could "clean up" the parts of the law he thought were unconstitutional.

"To avoid an incongruous legal 'black hole' at Guantanamo, this Court should strike down the MCA's illegal suspension of the Great Writ and allow Congress to establish procedures consistent with what national security and the Constitution require," Specter wrote.

Four conservative legal organizations support the Bush administration, urging the court not to use what the Washington Legal Foundation calls its "raw power" to overturn the work of Congress and the president.

Justice Anthony M. Kennedy, who was the deciding vote last year in the court's most controversial cases, appears to be in the spotlight again; Kathleen M. Sullivan, director of the Constitutional Law Center at Stanford University, jokingly referred to the carefully tailored briefs in the case as "love letters to Justice Kennedy."

Kennedy is believed to have provided the key fifth vote required for the court to consider the latest detainee case. In his concurring opinion in the 2004 Rasul, he acknowledged the difficulty the court faces in times of war.

"There is a realm of political authority over military affairs where the judicial power may not enter. The existence of this realm acknowledges the power of the President as Commander in Chief, and the joint role of the President and the Congress, in the conduct of military affairs," Kennedy wrote.

But he added that the "necessary corollary" is when courts "maintain the power and the responsibility to protect persons from unlawful detention even where military affairs are implicated."