ASHINGTON, June 1 - The Supreme Court reinstated a 17-year-old's murder conviction on Tuesday, ruling 5 to 4 that the California courts were not wrong to disregard his youth in deciding that the police were not obliged to read him his Miranda warnings before questioning him.

The teenager, Michael Alvarado, was not under arrest during the two-hour interrogation, which took place in a police station interrogation room. Under persistent questioning, he confessed to taking part in a carjacking that led to the driver's murder. Mr. Alvarado, who was brought to the station by his parents at the request of the police, was not given the familiar advice about his right to remain silent and to consult a lawyer.

The Supreme Court's landmark decision in Miranda v. Arizona applies only to interrogation of someone in custody, so the question for the California courts was whether Mr. Alvarado was "in custody" for purposes of applying the Miranda rule even though he was never told that he could not leave. Both the trial judge, who rejected his motion to suppress his incriminating statements, and the California Court of Appeal, which affirmed his conviction, concluded that he had not been in custody.

At the federal court level, where Mr. Alvarado then sought a writ of habeas corpus, the question was a different one: not whether he was in custody, but whether the state courts had reasonably concluded that he was not.

A 1996 federal law, the Antiterrorism and Effective Death Penalty Act, sharply circumscribed the authority of federal courts to review state-court criminal convictions, limiting their jurisdiction to those state-court proceedings that "resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established federal law." So to invalidate his conviction through a writ of habeas corpus, Mr. Alvarado had to convince a federal court that the determination that he had not been in custody was unreasonable.

The Federal District Court in Los Angeles rejected his argument, but the United States Court of Appeals for the Ninth Circuit accepted it in the 2002 decision that the justices overturned on Tuesday. The Ninth Circuit had held that the state courts had failed to consider Mr. Alvarado's youth and inexperience with the criminal justice system. A reasonable person in his circumstances would not have felt free to leave, the appeals court said, applying the "reasonable person" test for custody that the Supreme Court's Miranda decisions have developed.

Addressing the question of its own jurisdiction under the 1996 law, the Ninth Circuit then said that although the Supreme Court had never explicitly considered youth as a factor in analyzing a Miranda custody case, the justices had treated youth as relevant in other criminal contexts. Consequently, the appeals court held, it was an "unreasonable application" of the "clearly established law" on juvenile status for the state courts to have failed to consider Mr. Alvarado's youth in deciding how he reasonably would have responded to the circumstances of the interrogation.

California's appeal to the Supreme Court, Yarborough v. Alvarado, No. 02-1684, raised an issue that transcended the particulars of the case, making the appeal significant for the broader question of federal court jurisdiction to review state convictions. That question was whether a failure to extend an established legal principle to a new context can ever be regarded as an "unreasonable application of clearly established federal law."

The state argued that a "failure to extend" is never unreasonable. This argument did not fully prevail on Tuesday. Writing for the majority, Justice Anthony M. Kennedy said "the difference between applying a rule and extending it is not always clear." He added, "Certain principles are fundamental enough that when new factual permutations arise, the necessity to apply the earlier rule will be beyond doubt."

But the majority agreed with California that this was not such a case. There were arguments on both sides, Justice Kennedy said, and "fair-minded jurists could disagree over whether Alvarado was in custody." But he added that it was reasonable for the state courts to conclude that he was not, given that "our court has not stated that a suspect's age or experience is relevant to the Miranda custody analysis." He added, "the state court's application of our law fits within the matrix of our prior decisions" and so barred the federal courts from granting a writ of habeas corpus.

The majority opinion was joined by Chief Justice William H. Rehnquist and by Justices Antonin Scalia, Clarence Thomas and Sandra Day O'Connor. Justice O'Connor also wrote a concurring opinion. She said there might be cases in which age is a relevant factor in the custody determination, but said the California courts could reasonably have concluded that this case, with Mr. Alvarado nearly 18 years old, was not one of them.

In a spirited dissenting opinion, Justice Stephen G. Breyer said the majority opinion defied "ordinary common sense." He asked, "What reasonable person in the circumstances - brought to a police station by his parents at police request, put in a small interrogation room, questioned for a solid two hours, and confronted with claims that there is strong evidence that he participated in a serious crime, could have thought to himself, 'Well, anytime I want to leave I can just get up and walk out?' "

Justice Breyer concluded, "Unless one is prepared to pretend that Alvarado is someone he is not, a middle-aged gentleman, well versed in police practices, it seems to me clear that the California courts made a serious mistake."

Justices John Paul Stevens, David H. Souter and Ruth Bader Ginsburg also signed the dissent.