"Palimony," the press dubbed it, when California Judge Arthur K. Marshall awarded Michelle Triola $104,000 to "rehabilitate" herself to something near the position she could have expected if she hadn't given up her singing career to spend six years living with actor Lee Marvin. "Gallimony" is what a New York newspaper called the support for which Marilyn Barnett sued tennis star Billie Jean King.

"Acrimony" is the term favored by Leonard Graff, an attorney handling a Washington, D.C., homosexual palimony case.

The press given these palimony cases has focused public attention on a major shift in American law -- the opening up of courtroom doors to disputes between unmarried couples, particularly former live-in lovers who have decided to call it quits. Many couples who previously enjoyed the no-strings-attached freedom of living together out of wedlock are now taking a new look at their joint bank accounts and tenancies-in-common. Here is why.

Until Marvin v. Marvin and other cases like it, unmarried couples who disagreed about rights to income or property had -- except in common-law marriage -- no recourse to the courts. As Triola's attorney, Marvin Mitchelson, explains in his handbook called Living Together:

"Our of our Puritan heritage came a guiding principle in the law that sex is legal only within the bonds of marriage."

In this context, the courts have always found that couples who live together out of wedlock were guilty to start with and therefore deserved no legal remedy. They could not enter domestic relations court because they were not married, and they could not enter the civil court because no promise or agreement could be enforced if it involved living in sin.

When the case of Marvin v. Marvin arose in 1970, Michelle Triola was, according to Mitchelson, a "meretricious spouse in a state that didn't recognize common-law marriage. She was, in the eyes of the law, a prostitute, and no agreement she might have could be enforced."

Domestic court was not available to her, so in 1972 attorney Mitchelson filed suit on her behalf in civil court, alleging that Lee Marvin had breached an express oral contract to share equally in about $2 million worth of property they had acquired together between 1964 and 1970.

The trial court dismissed her suit on the grounds that no agreement between her and Marvin was enforceable because she was a meretricious spouse.

Mitchelson appealed to the California Supreme Court, which rocked the legal world with its landmark decision in December 1976, stating basically that the courts should enforce express agreements between nonmarital partners (except to the extent that their contract is explicitly founded on the consideration of sexual favors); that in the absence of an express contract the courts may find that the conduct of the parties demonstrates an implied contract or agreement; and that the courts may apply the legal doctrine of equitable remedies should the facts of the case support such a ruling. Specifically, the higher court decided that Triola was entitled to a trial on her contention that she and Marvin had an express oral agreement to share community property.

Legal opinion is divided on the merits and implications of the Marvin decision, but courts in at least 28 states have reviewed it and courts in only three states -- Georgia, Illinois and Maine -- have rejected the palimony concept.

But while states may be cracking open courtroom doors for litigation between heterosexual couples living together, there's still some question about whether similar rights will be extended to homosexual couples.

The D.C. Superior Court dismissed in 1979 the first homosexual palimony suit, Cox v. Elwing, on the grounds, loosely, that cohabitation is against public policy in the District of Columbia. (The same principle could be applied to heterosexual couples in jurisdictions where cohabitation or fornication between unmarried couples are technically against the law, as they are in D.C. and Virginia. The issue did not arise in Marvin v. Marvin because they are not against the law in California.)

The ruling on Cox v. Elwing is currently before the D.C. Court of Appeals, where attorneys for both sides feel the lower court's decision to dismiss the case will probably be overturned.

In a second case, in New York City, John Michael Tebelak is claiming that Richard Hannum, author of the play "Godspell," agreed to support him for life in return for the housekeeping and other assistance he rendered Hannum during the seven years they lived together.

What makes the success of most palimony cases unlikely is the difficulty of proving, when no written agreement exists, that someone has agreed orally to support or share property with his or her unmarried partner in return for legitimate considerations.

No one knows for certain where "palimony" law is headed, although it's fairly certain to show up eventually on the Supreme Court docket. A whole round of secondary problems has already arisen.

What happens, for example, if a man agrees to leave his wife, marry his mistress and support her for life, and then reneges on his promise, a claim made in a Los Angeles case, Maynard v. Priester.

And if live-together lovers are eligible for palimony, what are a spouse's alimony obligations if his or her ex-spouse moves in with a lover in a de facto marriage? Can someone collect alimony as well as palimony?

Although the outcome of the various palimony cases will vary from jurisdiction to jurisdiction, they all have one thing in common: Most lawyers are unlikely to handle them unless the defendant in the suit is a client with what is known in the trade as "deep pockets."