The East German Government, at great expense, has purchased a male gorilla to mate with a female gorilla already in captivity at the East Berlin Zoo. But the male, it turns out, will not preform his duties, "not even for Western money.Not even after being shown Communist Party documents on his role, and not even after being shown training films, which he laughs at. He's being human, like you and me," an East German tells visitors here.

On the evening television newscast, the lead item is about a cockroach invasion of Dresden's newest international hotel and a race to the kitchen in which the Soviet team overwhelmed the competition. Then, the newcast switches to Moscow for a special reports from the East German correspondent there who reports that the Soviets have just announced development of a new breed of cockroach able to inseminate a blossom at 10,000 feet altitude without wearing a hat or muffler.

The anecdotes about the gorilla and the TV evening news are, of course, spoofs. But they are typical of the rare bursts of private humor and fun-poking that take place in the handful of political cabarets that dot the generally humorless and officious political landscape of Communist East Germany.

Here in Dresden, the shows go on at the "Herkuleskeule," a double-meaning name which means Hercules Clubs, but a club is also something that people can get hit over the head with.

In East Berlin, the cabaret is called "Distel," sort of a prickly thistle, and in Leipzig, it is the "Pfeffermuehle," which is perhaps the best known in the country.

Wherever they are, they are hard to get into. People wait months and even a year for a pair of tickets, sometimes trading them for a badly needed automobile spare part that otherwise would require waiting in long lines to get.

The rooms are intimate, with usually 150 or so guests. It is a well-dressed and sophisticated audience, though a Communist Party member "guide" who accopanied a Western newsman to the club here said a lot of the listeners also were "workers." At our table were two other couples, two doctors and two newspaper editors.

These are not the anything-goes wildly decadent cabarets of the pre-Hitler '30s as immortalized by Cirstopher Isherwood in "I Am A Camera" and its musical version, "Cabaret."

Throughtout Eastern Europe, the political cabaret and private humor is a highly developed art form, a safety valve, in effect, for the authors of the skits, the performers, and that apart of the population that needs to let is intellect enjoy a knowing relationship with something oterh than the relentless outpouring of official propaganda.

Everywhere in East Germany these days, for example, there are red and white posters exhorting people to keep working hard for the great strides of socialism and for the great brotherhood with the Soviet Union that will be commenmorated again this October when East Germany marks its 30th anniversary.

"Everywhere you look these days you see 30," quips a performer here. "Is that the speed limit or does it mean we're important?" he asks.

The shows usually run for two hours and they are very slick, irreverent and fast-moving, reminiscent of te heyday of Greenwich Village supper clubs in New York in the 1950s when the rising young satirists of American tastes and values began to make a dent on public opinion.

Here, and elsewhere in the East, however, these cabarets play an even more important outlet because there are few other outlets.

The performers are clever, mocking the party, the bureaucracy of the labor unions, and the Russians. Usually they do it in a careful way that seems to keep them safe, give the government enough room to let the shows go on, yet bring an even more knowing laughter from an audience that doesn't have to have things spelled out in red and white for it.

Last week, however, it was reported that government authorities had forced cancellation of the current show at the Pfeffermuehle, illustrating the thin line that is often walked here. Party functionaries apparently raised objections to material in the cabaret's 25th-anniversary show and forced the first shutdown since 1964. It was not known if a revised version will be performed instead.

The canceled show reportedly had a scene in which party chief Erich Honecker makes an unannounced visit to a married couple in the midst of a divorce, and at another point refers to East German citizens as "people in a preservin jar."

The West, too, and its ways also are taunted here as are even the Socialist brothers in the third world. "When you see those big Western cars at the universities here these days," the audience is told, "you can no longer just assume it belongs to a professor. More likely it belongs to the students from the developing countries."

The East German media, which are totally state-controlled, is mocked in a skit which shows provincial people straining to see what all the fuss is about in town over an official visitor whom they cannot see. But it doesn't matter because they will read about how much they love him in tomorrow's paper.

Though East German probably live better than most of their comrades in the East Bloc, there are some things that are not so good. So one performer warns about letting coffee fall on your head, not because it will burn but because the "mixed blend" sold here is so heavy.

Another notes that East Germans are the world's greatest per-capita eaters of butter and also big meat eaters and that, in fact, they seem to have already eaten their 1980 supplies, a reference to reports of meat shortages in some areas of the country.

At another cabaret, a visitor here relates, the audience is asked how party chief Honecker can tell which one of the many telephones on his desk is the hot-line to Moscow. "It is the one with only an earpiece," he answers.

Any why is East Germany importing 10,001 Volkswagen cars from West Germany, anothe cabaret line goes. "That is so no one can say they are only meant for the upper 10,000 of East German society."

Another Western newsman, Leslie Colitt of The London Financial Times, who visited the Pfeffermuehle in Leipzig last year, reported a skit in which an East German laborer who insists he can fly is called in to explain himself to his foreman. The laborer feels he could help the factory by flying in badly needed spare parts. The foreman tells him there is no place in the paln for that and then a trade union representative informs the laborer that the laborer doesn't understand the deeper causes of his wanting to fly. "You see, you're acting spontaneously," the official points out, a serious accusation in a tightly controlled bureaucracy.

At another point in the Pfeffermuehle show, it was reported, one performer says to another, "In the interests of socialist solidarity, we must unite with our audience." "Exactly, united we shall land in prison," the other perfomer replies. "If you didn't write that line, then who did?" the first perfomer asks, a subtlety that draws laughter from an audience aware of the sensitivity of the government ot he slightest hint of opposition and behind-the-scenes plotting to undermine the establishment. CAPTION: Picture, Liza Minnelli in "Cabaret"