Russian playwright's satirical look at life in Soviet bureaucracy; The Nest of the Wood Grouse. Play by Victor Rozov. Translated by Susan Layton. Directed by Joseph Papp.

The Soviet comedy receiving its American premiere at the Public/-Newman Theater transports the spectator to Moscow for the weeks from April to May Day in the early 1970s. Playwright Victor Rozov takes an amused look at his nation's new bourgeoisie - the bureaucrats who have mastered the intricacies of a Byzantine dictatorship. For their enterprise, they enjoy comforts and luxuries unshared by the great proletariat.

Sudakov (Eli Wallach), the head of Mr. Rozov's particular Moscow household, is a middle official in the Foreign Office. When a visiting Italian emissary (complete with official interpreter) pays a courtesy call, Sudakov observes blandly that the visitor is being given ''a chance to look at an average Soviet family.'' This ''average'' family occupies a handsomely furnished flat of six rooms - achieved by joining the Sudakovs' quarters to those of their daughter and son-in-law.

Ironies abound in Mr. Rozov's genre comedy. If not lethal, the satire is sufficiently sharp to prompt some surprise that (according to a program insert) ''The Nest of the Wood Grouse'' is ''playing to capacity audiences at the Satire Theatre in Moscow.'' In a typical line, Sudakov informs the Italian: ''We have freedom of religion. None of my family is religious.'' He explains that the present Soviet credo, ''From each according to his ability, to each according to his work,'' will someday end ''to each according to his needs.''

The obliging bureaucrat is busily engaged in doing favors for fellow bureaucrats in return for favors past or to come. The score is scrupulously kept. Although bootlicking is standard practice, when the son of his superior commits suicide, Sudakov is so concerned about coming under the shadow of his boss's disgrace that he skips the funeral.

It develops that the Sudakovs have nurtured a viper in their midst. Having married into the family to advance his career, son-in-law Georgy (Dennis Bout-sikaris) is preparing to divorce out of it in anticipation of a better match. This is but one of the plot lines that Mr. Rozov unfolds in an entertainingly old-fashioned way and with a cast of characters more numerous than most Broadway commercial managements could afford.

The production staged by Joseph Papp of Susan Layton's idiomatic translation communicates with apparent faithfulness the atmosphere and flavor of this particular Moscow milieu.To be sure, some of the play's themes are universal: the generation gap, the prevalence of autocrats, the passing squalls in a happy marriage, and the contretemps that have more to do with ideals than ideology. When Georgy observes that people with principles are hard to get along with, his unhappy wife replies: ''People without principles are dangerous.''

Mr. Wallach is splendidly fussbudgety as the harried Sudakov and Anne Jackson presents Mrs. Sudakov as the kind of strongly maternal figure who can shift instantly from giving tea and sympathy to barking out orders like the Army nurse she used to be. Mary Beth Hurt is movingly self-contained as daughter Iskra, a woman betrayed in more ways than one by the man she has loved. Ricky Paull Goldin's teen-age son Prov proves fresh enough to irritate his father and troubled enough to risk a close shave with the law. Phoebe Cates's pretty predator schemes unabashedly, and Mr. Boutsikaris makes Georgy a very nasty climber.

Assorted incidental characters lend local color, add to the prevailing liveliness, and occasionally come to the rescue of the leisurely plot. They include Rosemary De Angelis as the blowsy but good-hearted mother of Prov's girlfriend, Julie Cohen as the girlfriend, Rebecca Schull as an old Sudakov flame in need of a favor, Jacqueline Bertrand as an interpreter who falters only when it come to jokes, and Ernesto Gasco as the voluble visiting Italian. The casting throughout is exemplary.

Loren Sherman's setting accommodates the Sudakovs in a style worthy of a decadent capitalist and Theoni V. Aldredge has costumed the comedy with her usual flair. Arden Fingerhut's lighting matches the cheerful mood.

A program note explains the play's title as follows: ''Because the male wood grouse (capercaillie) experiences temporary deafness during its mating ritual, the name of the bird in Russia is also applied to a person who is hard of hearing.'' In Mr. Rozov's comedy with serious undertones, everyone talks while not everyone listens. But perhaps the playwright wants to catch Big Brother's ear.