ASHINGTON, April 25 - The Supreme Court agreed on Monday to decide whether a convicted murderer has the right, during the penalty phase of the trial, to present evidence that casts doubt on the jury's finding of guilt in an effort to avoid a sentence of death.

The court accepted a death-penalty case from Oregon to answer a question that has divided the state and lower federal courts in the years since an ambiguous Supreme Court opinion addressed it in 1988. The state is appealing a ruling by the Oregon Supreme Court that gave a defendant the right to present evidence of an alibi that, if accepted in the penalty phase, would show that he could not have been at the scene of the double murder for which the jury had just convicted him.

The Supreme Court's precedents make clear that in a capital murder trial's penalty phase, which has many attributes of a separate trial, the defendant must be able to offer "any aspect" of his personal background or of the circumstances of the offense to show why a death sentence would be inappropriate.

The one exception has been evidence offered to demonstrate lingering doubt about the guilty verdict itself. In its 1988 decision, the Supreme Court held that a defendant did not have a constitutional right to have the judge instruct the jury that it should consider any "residual" doubt about guilt when deciding on a sentence.

But that decision, Franklin v. Lynaugh, did not address the more basic question of whether, aside from the eventual jury instructions, the defendant had the right to present such evidence to the jury in the first place. That question, which has confused the lower courts, is the issue the justices have now agreed to decide in Oregon v. Guzek, No. 04-928, the case they accepted on Monday.

The defendant, Randy Lee Guzek, was convicted in 1988 of murdering the aunt and uncle of his former girlfriend. He was sentenced to death, but the Oregon courts vacated his death sentence in 1990 and again in 1991, ordering new proceedings as the result of United States Supreme Court decisions in other death penalty cases. Each time, Mr. Guzek was re-sentenced to death.

In 2004, the Oregon Supreme Court once again overturned the death sentence, finding several errors. It ruled that in any subsequent hearing, Mr. Guzek should be permitted to present transcripts of statements from his mother and grandfather that were admitted during the guilt phase.

Taken together, the two statements provided an account of Mr. Guzek's whereabouts on the night of the murder that, if credited, made it highly unlikely that he had been at the murder scene. The state court's 3-to-2 decision held that Mr. Guzek had a right to present the evidence of his alibi under the Eighth Amendment, which prohibits cruel and unusual punishment.

The issue in the case, which will not be argued until next fall, might have some bearing on the forthcoming death penalty hearing for Zacarias Moussaoui, who pleaded guilty last week to taking part in the conspiracy that led to the Sept. 11, 2001, terrorist attacks. While pleading guilty to a capital offense, Mr. Moussaoui announced his intention to contest the death penalty. Judge Leonie M. Brinkema of Federal District Court, who has presided over the case, said Friday that access to high-level Qaeda detainees could provide mitigating evidence for Mr. Moussaoui and would be "highly relevant to the sentencing phase." Mr. Moussaoui has long claimed that these witnesses, to whom the government has denied him access, would exonerate him.

There were also these developments at the court on Monday.

Postal Negligence

The court agreed to resolve a dispute among the lower federal courts over the government's liability for negligent mail delivery. Under the Federal Tort Claims Act, the government is immune from liability for "any claim arising out of the loss, miscarriage, or negligent transmission of letters or postal matter." The question in this case, Dolan v. United States Postal Service, No. 04-848, is the meaning of "negligent transmission."

The plaintiff, Barbara Dolan, fell and injured her back when she tripped over packages that a letter carrier had left on the porch of her home. The Federal District Court in Philadelphia, in a decision affirmed by the United States Court of Appeals for the Third Circuit, dismissed her suit on the ground that "transmission" includes the actual delivery of the mail, which could thus not be the basis for a lawsuit. By contrast, the Second Circuit, in New York, has interpreted the phrase "negligent transmission" as limited to loss or damage to the mail while in transit.

P.O.W. Lawsuit

Without comment, the justices refused to hear an appeal brought on behalf of 17 American prisoners of war from the Persian Gulf war of 1991. Along with their families, the 17, who were tortured in Iraqi prisons, sued Iraq under a federal law that permits such suits against officials of governments that have been designated as state sponsors of terrorism.

In 2003, after Iraq failed to respond to the lawsuit, a federal judge in the District of Columbia, Richard W. Roberts, awarded the plaintiffs nearly $1 billion. The federal government opposed the judgment and the United States Court of Appeals here overturned it last June, dismissing the suit on the ground that the plaintiffs lacked a proper basis for invoking the law.

In their appeal, Acree v. Republic of Iraq, No. 04-820, the plaintiffs said the decision, "if left uncorrected by this court, will pose a serious and potentially insurmountable obstacle for future victims of terror." But the solicitor general's office said a large monetary judgment against Iraq, now viewed as "a state subject to our protection" rather than an enemy, would "hinder crucial foreign policy objectives." The government's brief added, "After the new Iraqi regime has had time to become firmly established, the president may choose to espouse petitioners' claims through diplomatic means."