Adaptation--Next -- Two very funny and chilling plays, both directed by Mike Nichols' brilliant ex-partner, Elaine May. The first one-acter, written by Miss May, shows the game of life as seen in terms of a TV quiz show. The second, by Terrence McNally (a perverse playwright's perverse playwright, and happily so), is about a 48-year-old man undergoing a humiliating army physical. Gabe Dell and James Coco--two of the best actor-comedians around--play the leads. At the GREENWICH MEWS THEATRE, W. 13th St. (243-6800).

Big Time Buck White--Joseph Tuotti's play, which grew out of the Budd Schulberg Watts project, is about an organization called B.A.D. (Black Alleluia Days) and a handful of its members. The doings of these members--who embrace black culture while simultaneously trying to get a grip on the monetary aspects of white culture -- while setting up for a meeting are howlingly funny and true. When the title character, their leader, arrives to answer race-oriented questions, things get a little stagey. The production, which is graced by what may be the best cast in New York, closes Sunday; do not miss it. At the VILLAGE SOUTH THEATRE, 15 Vandam St. (989-7736).

Boys in the Band--A devastating concoction of humor and biterness centered around a homosexual birthday party. The action and dialogue (by Mart Crowley) are grimly explicit, and the all-new cast (under Robert Moore's flawless direction) should be as good as their original counterparts. Totally engrossing, painful, and should not be missed. At THEATRE FOUR, W. 55th St. (246-8545).

Cabaret--This musical about the degeneration of German society just before Hitler came to power is a heady production emblazoned in the tones of Kurt Weill and George Grosz. Most of the original cast is gone, but the Kander-Ebb score, the Boris Aaronson sets, and Harold Prince's direction--all miraculous--are still there. So is Lotte Lenya, who is as beautiful and gravel-voiced as ever. At the BROADWAY, Broadway at 53rd (247-7992).

Cop-Out--As of now, a blind item (since it is still giving low-priced previews), this work by John Guare (author of last year's "Muzeeka") looks promising. At the CORT, W. 48th St. (CI 5-4289).

Dames at Sea--An ingenious musical spoof of the kind of entertainment Busby Berkeley, Dick Powell, Ruby Keeler and Joan Blondell used to provide during the depression: a lot of fun. The cast includes a lovely girl with a weird voice who goes by the name of Bernadette Peters. At the BOUWERIE LAND THEATRE, 330 Bowery at 2nd St. (674-6060).

Dionysus in '69--Richard Schechner's strange and fascinating version of Euripides' "The Bacchae." At the PERFORMING GARAGE, 33 Wooster St. (WA 5-8712).

Fiddler on the Roof--Now in its fifth year and still in great shape, this powerful Stein-Bock-Harnick-Robbins drama weaves Sholom Aleichem's "Tevye" stories into a panoramic view of the breakdown of tradition in Russian-Jewish society. Harry Goz is the present Tevye, and well up to snuff. At the MAJESTIC, W. 44th St. (246-0730).

Frankenstein--Tonight and Saturday the Living Theatre gives its final performances in America for a while. This may not be the best of their productions and you may hate Julian Beck's troupe anyway--but their antics are worth looking at, at least once. At the BROOKLYN ACADEMY, 30 Lafayette Ave. (ST 2-2434).

The Great White Hope -- James Earl Jones' performance as black prize-fighter Jack Johnson is awe-inspiring--and makes a visit to this production worthwhile. But the play (by Howard Sackler) is generally awful and sometimes offensive -- unfocused, full of wretched excesses, and sociologically more pertinent to the forties than the sixties. Edwin Sherin's direction isn't much either, nor is the supporting cast--with the exception of Lou Gilbert as a much-tormented manager. At the ALVIN, W. 52nd St. (757-8646).

Hadrian VII--Alec McCowen's performance as a neurotic-intellectual-homosexual who dreams he becomes Pope is every bit as great as everyone says it is. Peter Luke's script is solid, entertaining, and happily devoid of philosophical pretentiousness. At the HELEN HAYES, W. 46th St. (246-6380).

Hair--A hippie "Hellzapoppin" with a lot of spirit and a nice score firmly based in the vocabulary of early rock. Only when the authors try too hard to explain to our parents what the new culture is all about do things become a little thick. Tom O'Horgan is the director, and the nice cast includes Barry McGuire and the nice Heather MacRae. At the BILTMORE, W. 47th St. (582-4340).

Inner Journey--Hardly great, but still an interesting play by James Hanley. Jules Irving directed and the redoubtable Michael Dunn is in the cast. At THE FORUM, Lincoln Center, W. 65th St. (EN 2-7618).

In the Matter of J. Robert Oppenheimer--A quasi-documentary by Heiner Kipphardt about the hearing in which Dr. Oppenheimer lost his security clearance. Hebert Berghof is in it and so is Joseph Wiseman (in the title role), an actor who never ceases to amaze. At the VIVIAN BEAUMONT, Lincoln Center, W. 65th St. (362-7216).

Invitation to a Hanging--A mixed bag with some style from the New York Shakespeare Festival. The play is adapted from a Vladimir Nabokov novel, the cast includes Joe Bova and John Heffernan, and the director is Gerald Freedman. At the PUBLIC THEATRE, 425 Lafayette St. (677-6350).