The Supreme Court begins its 1987-88 term Monday confronting a number of controversial cases involving abortion, school prayer and the death penalty, and with a possibly deadlocked eight-member court for most, if not all, of the term.

The increasingly doubtful confirmation of Robert H. Bork to succeed retired justice Lewis F. Powell Jr., in recent years the court's swing vote, could result in a stalemate in dozens of the most sensitive cases. The court last year split 5-to-4 in 43 of 150 cases, and Powell cast a deciding vote -- or at least was in the majority -- 34 times.

If the justices tie in a case, the lower court ruling stands but there is no nationally binding precedent. The justices may decide to hold a closely divided case until a ninth justice is sworn in -- whether that is later in the same term or in the next term.

This is the fourth time in the last 18 years that the justices have, in effect, convened with fewer than nine justices. On each previous occasion, the remaining justices decided as many cases as they could, putting off the most important cases until the court was at full strength and letting some cases come down as ties.

The absence of a ninth justice also may affect the cases the court decides to hear for the rest of the term. Under the normal working arrangement, the court will agree to hear a case if four justices, one short of a majority, want to do so. That rule stays in force whether there are eight or nine justices.

Having only eight justices may make it more difficult for some litigants to garner the minimum four votes to have the court hear their appeals. When there are only three votes to take a case on an eight-member court, the justices have often held the case, sometimes for months, for consideration by the ninth justice.

The court was shy one justice for almost all of the 1969-70 term. Justice Abe Fortas resigned in May 1969, and Justice Harry A. Blackmun did not take his seat until June 1970. After he did, 18 cases were reargued before the full court.

The court operated with seven justices for nearly half the 1971-72 term, after Justices Hugo L. Black and John M. Harlan retired in September 1971. Justices Powell and William H. Rehnquist did not replace them until January, 1972. Once they were on the court, a number of cases, including Roe v. Wade, the landmark abortion case, and the court's most important obscenity ruling, were reargued.

In the most recent occasion, the court was officially at full strength but the justices decided not to count the vote of Justice William O. Douglas, who was officially on the court but disabled by a stroke, for the first three months of the 1975-76 term. Justice John Paul Stevens was sworn in on Dec. 17, 1975.

The court already has some experience working without Powell. He missed oral argument in 56 cases during the 1984-85 term, when he underwent surgery for prostate cancer. The court deadlocked 4-to-4 in eight of those cases; five others, according to court records, were reargued.

Although no other retirements appear imminent, the court's three oldest members were hospitalized over the summer.

Justice William J. Brennan Jr., 81, the court's senior liberal, returns after medical treatment for an enlarged prostate. Justice Thurgood Marshall, 79, was hospitalized recently after developing a blood clot in his foot. And Justice Blackmun, 78, underwent radiation treatment for a recurrence of prostate cancer.

The 84 cases selected for this term involve important, highly controversial issues. But they do not call for fundamental alterations in the most controversial rulings of the last 35 years involving sensitive social issues such as prayer in public schools, abortion, civil rights and criminal justice.

The court in recent terms has been, for the most part, fine-tuning earlier rulings in those areas. Those issues are before the justices again, but the questions raised are not fundamental.

Neither side in the abortion case is asking the high court to overturn the constitutional right to abortion. Neither side in the school prayer case is asking the court to overturn its decisions banning teacher-led prayers. And neither side in the major death-penalty case expects the court to alter its view that capital punishment is constitutional.

"If there were ever a term to have eight justices, this might be the one," said Harvard Law School Prof. Laurence H. Tribe.

Still, some controversial cases in the lower courts may reach the high court by the end of the term.

The most controversial involves the constitutionality of the law establishing an independent counsel or special prosecutor to investigate charges of wrongdoing by senior government officials.

Several officials under investigation, including former White House aide Marine Lt. Col. Oliver L. North and former White House deputy chief of staff Michael K. Deaver, have challenged the law on the grounds that it violates the constitutional requirement of separation of powers among the three branches of government.

Another highly controversial case that may be heard this term involves a law that allowed federal funding for religious organizations that counsel teen-agers to avoid sex. A federal judge here struck down the law as a violation of the required separation of church and state.

The abortion case, Hartigan v. Zbaraz, asks the court to decide the constitutionality of an Illinois law requiring minors who seek abortions to notify their parents and wait 24 hours for an abortion. An appeals court in Chicago struck down the law, which is similar to laws in 22 states. The case will be argued Nov. 3, probably before an eight-member court.

"Pro-choice" groups had hoped the court, with Powell providing the fifth vote, might strike down the law as an unconstitutional infringement on a right to abortion. With Powell gone, it is likely that the court will split 4-to-4, letting the lower court ruling stand. That would be the outcome, provided the justices can get around certain technical legal problems in the case, something many observers are not sure they can do.

Another case, Karcher v. May, involves the constitutionality of a New Jersey law requiring a moment of silence at the beginning of each public school day.

Two years ago the court struck down as unconstitutional a similar Alabama law, finding that the purpose of the law was religious, a vehicle for getting teacher-led prayer back into the public schools.

But the justices said that a majority might find other "moment of silence" laws constitutional.

That case, however, also has some difficult procedural questions that may make it difficult for the justices to render a definitive ruling on the constitutionality of such laws.

Death-penalty opponents will be hard-pressed to muster five votes in a case challenging the constitutionality of the death penalty for juvenile murderers. Powell, who upheld the constitutionality of capital punishment in general, nevertheless frequently voted to bar it when defendants were not given substantial procedural protections and every conceivable opportunity to present their best defenses.

The case before the court, Thompson v. Oklahoma, to be argued in November, involves William Wayne Thompson, who was 15 years old when he and three adults murdered a man in 1983. About 37 of the 1,900 death row inmates nationwide have been sentenced to die for crimes committed before age 18. Since 1982, three persons have been executed for murders committed before they were 18 years old.

Because only two members of the court, Justices Brennan and Marshall, think the death penalty is unconstitutional, the Thompson case is likely to produce at best a narrow ruling.

The court will decide a number of important cases this term involving freedom of speech.

One case, Reagan v. Abourezk, asks whether the government can deny visas to people allegedly linked to Communist governments who have been invited to speak in this country.

Another case, Boos v. Barry, asks whether the District of Columbia may forbid protest demonstrations within 500 feet of embassies. Opponents of the law say that it unconstitutionally favors those who support a foreign government's policy and blocks those who want to show their opposition to it.

A third free-speech case, from Virginia, involves an anti-obscenity law -- struck down by a judge as too broad -- that banned the display of material that might be deemed "harmful to juveniles."

The law was supposed to force newsstands and bookstores to hide from view the covers of sexually explicit magazines such as Playboy, Penthouse and Hustler. The case is Virginia v. American Booksellers Association.

The court will also be asked to decide whether high school officials in Hazelwood, Mo., violated students' free-speech rights when they censored a school newspaper article about teen pregnancy and students' views on divorce. The case is Hazelwood School District v. Kuhlmeier.