As the Supreme Court prepares for today's oral arguments on the federal "partial birth" abortion ban, both sides are focusing on the same question: "What will Kennedy do?"

Four liberal justices are considered certain votes against the law, legal analysts said, and four conservatives are expected to uphold it. The pivotal figure in the biggest Supreme Court abortion battle in half a decade is Justice Anthony M. Kennedy, the 70-year-old centrist with an 18-year record of eclecticism on abortion and other social issues.

Abortion rights advocates believe that, despite his past support of a state ban on the late-term procedure that opponents call "partial birth," he may now assume the moderating "swing vote" role that retired Justice Sandra Day O'Connor formerly played. Kennedy's performance may not only determine the fate of this federal abortion law but also foreshadow the overall balance of power on a court that is still defining itself after the addition of two conservatives picked by President Bush.

"If he is the fifth vote, which is the conventional wisdom, we have to come up with something that explains why this case isn't like Stenberg v. Carhart," the 2000 case striking down a state ban, in which Kennedy dissented, said Stanford University law professor Pamela S. Karlan, who co-wrote a friend-of-the-court brief for California doctors opposing the ban.

Supporters of the ban are attempting to convince Kennedy of the opposite. "If you look at all the briefs, they are all written to Justice Kennedy," said Benjamin W. Bull, chief counsel of the Alliance Defense Fund, an antiabortion legal organization.

Solicitor General Paul D. Clement quotes Kennedy's Stenberg dissent 22 times in his briefs defending the federal law, which was adopted by a wide margin in Congress and signed by Bush in 2003.

Bush's conservative appointees, Chief Justice John G. Roberts Jr. and Justice Samuel A. Alito Jr., have thin track records on abortion, and some court-watchers say they may not be sure to vote to support the ban.

As chief justice, Roberts might have institutional concerns if the court appears to abandon a major abortion ruling that has been on the books for only six years.

"Roberts might be convinced by stare decisis," the legal principle that favors sticking with established precedent, Karlan said.

Liberal Justices John Paul Stevens, David H. Souter, Ruth Bader Ginsburg and Stephen G. Breyer were in the majority in Stenberg and are unlikely to switch.

Conservative Justices Antonin Scalia and Clarence Thomas are firm opponents of Roe v. Wade, the 1973 case that legalized abortion nationwide.

But Kennedy has been known to change his position on big issues.

Last year, Kennedy wrote the majority opinion in a 5 to 4 ruling that banned the death penalty for juvenile offenders. He had voted to uphold it 16 years earlier.

In a major 1992 abortion case, Planned Parenthood v. Casey, Kennedy voted at the justices' conference to uphold Pennsylvania's strict abortion regulations but later switched and cast a fifth vote to reaffirm Roe v. Wade, according to internal court documents in the late Justice Harry A. Blackmun's papers at the Library of Congress.

This time, though, opponents of the ban must overcome not only Kennedy's vote in Stenberg v. Carhart but also the emotional dissenting opinion that accompanied it, in which he blasted "a procedure many decent and civilized people find so abhorrent as to be among the most serious of crimes against human life."

The procedure, known medically as "intact dilation and extraction," or "D & X," usually occurs in the second trimester of pregnancy. A doctor partially delivers a fetus, then suctions out its brain and collapses its skull to permit the head to exit.

The Guttmacher Institute, a reproductive-health organization affiliated with Planned Parenthood, has called the procedure rare and said only 2,200 were performed in 2000. Abortion rights advocates say the procedure is necessary in a relatively few cases when a fetus has a fatal birth defect such as anencephaly.

But abortion opponents say that estimate is too low and that the operation is tantamount to infanticide. In 1997, Nebraska, like many other states, outlawed it except when necessary to save a mother's life.

But the Supreme Court, by a vote of 5 to 4, struck down Nebraska's law, because it lacked an exception to preserve a mother's health. The court also ruled it was so vaguely worded that it might also criminalize other second-trimester abortion procedures.

In his dissent, Kennedy argued that the court had violated his understanding of the compromise forged in the Casey ruling: that the core right established in Roe would remain but states would have meaningful power to regulate abortion.

Like Nebraska's, the federal ban lacks a health exception. The Republican-controlled House and Senate instead issued "findings," based on congressional testimony, that the procedure is never necessary to protect a woman's health. Supporters of the law say the Supreme Court must defer to those findings.

Abortion rights advocates say the findings are wrong because "D & X" sometimes poses less risk of infection or surgical mishap than a common alternative, "dilation and evacuation," in which the fetus is pulled apart before being removed from the uterus.

So far all federal lower courts to rule on the law have said its lack of a health exception violates Stenberg. As a result, the ban has never been in effect.

At the Supreme Court, abortion rights advocates hope Kennedy also feels bound by Stenberg, even though he opposed it at the time. They also believe Kennedy could be persuaded by new information about the need for a health exception that the court did not have before it ruled in 2000.

"This will appeal to Justice Kennedy's sense of wanting to look at the medical evidence," said Nancy Northup, president of the Center for Reproductive Rights, which represents Leroy Carhart, the Nebraska physician who also challenged that state's law six years ago.

The California Medical Association is trying another tack -- appealing to Kennedy's belief in states' rights.

The federal ban invokes Congress's authority to regulate interstate commerce. But the CMA's friend-of-the-court brief argues that Congress's commerce authority cannot trump the states' traditional regulation of medical practice -- a tradition Kennedy cited earlier this year in striking down a Justice Department effort to prevent Oregon doctors from prescribing lethal doses under that state's assisted-suicide law.

The CMA brief quotes passages from Kennedy's opinion noting that "regulation of health and safety is 'primarily, and historically, a matter of local concern,' " particularly when it comes to "the practice of medicine."

"If it weren't abortion, his opinion in the Oregon case would apply," said Karlan, who co-wrote the brief. "The hard thing in partial-birth abortion is that he has a visceral feeling and has already expressed distaste for the procedure."