Gunnar Graps belongs to a distinctly new breed of Soviet man: a home-grown rock star whose antics on stage delight his youthful fans but trouble the Kremlin's cultural commissars.

With a mop of thick brown hair and a rasping, sexy voice, 30-year-old Graps looks like a cross between Mick Jagger and Rod Stewart. His popularity seems to stem from his ability to convince his audience that he is doing his own thing while at the same time giving them a taste of once-forbidden Western pleasures.

The Magnetic Band, which Graps leads, is one of several dozen rock groups that have transformed the Soviet pop music scene over the past few years. At a recent concert by the band in Moscow, hundreds of teen-agers leapt to their feet, swaying and clapping to the music and punching their arms into the air in gestures of ecstasy.

"It's a revolution of the mind," remarked a Russian spectator -- recalling the time when vigorous movement on or off stage was prohibited and singers were expected to stick to uplifting themes such as love on a collective farm or the struggle for world peace.

According to official Soviet dogma, art should not merely reflect life, but play an active part in the construction of socialism. This cultural commandment is all but ignored by rock musicians like Graps. Their songs voice the frustrations of Soviet youth, expressing a sense of individualism and alienation from the system.

"I don't believe in promises, and I won't believe in the future. It makes no sense to believe in them anymore," goes a song by the Time Machine, the Soviet Union's most celebrated rock group. The same band also tells its fans to "wear a mask" for "it is only under a mask that you can remain yourself."

Soviet officialdom seems undecided about how to deal with the rock music phenomenon. It alternates between taming the rock bands by offering them official contracts and the chance to perform in public and attacking them in the press as ideologically subversive.

The high point of official tolerance came in the period leading up to the 1980 Olympics in Moscow. The Kremlin was pursuing a relatively relaxed cultural policy at that time and numerous Western entertainers -- from Elton John to Boney M -- were invited to tour the Soviet Union.

The first official Soviet rock festival was held in Tbilisi, the capital of Soviet Georgia, and gave a big impetus to many home-grown groups, Time Machine and Magnetic Band included.

Over the past few months, however, the cultural screws have been tightened again. The Communist Party paper Pravda attacked the rock bands for "betraying the spirit of popular music by mindless adaptations" of Western songs. It described with distaste how young fans were being led astray by "the pulsing lights, smokescreens and the convulsive rhythms of the music."

The Pravda article, published in May, said that a Ministry of Culture conference devoted to pop music had resulted in "heated arguments and exchanges of opinion."

The dilemma facing the Kremlin is that, if it makes life too difficult for the rock groups, it risks driving them underground and losing touch with the young people they represent. The dilemma facing the musicians, on the other hand, is that a large part of their appeal lies in their antiestablishment image. They risk losing the loyalty of their fans if they accept official sponsorship too readily.

The result is an uneasy relationship in which each side needs and mistrusts the other. It is reflected in the fact that, while many of the groups are household names here and appear regularly on television and radio, it is virtually impossible to buy an album by Time Machine or Magnetic Band at Soviet record shops.

To appear in public at all, the rock groups are obliged to work through a monopoly state agency known as Philarmonia. Philarmonia arranges concerts and television appearances and provides much of their equipment. It also pays the musicians a regular salary, around 700 rubles ($900 dollars at the official rate of exchange) a month in the case of top-flight performers like Graps.

If a rock group steps out of line and is dropped by Philarmonia, it is effectively prevented from performing in any concert hall in the country.

Even more important than Philarmonia, however, is the unofficial music network. The real test of a rock star's popularity lies in the number of homemade cassettes of his songs that are in circulation -- and the price they command on the black market. Thus, while relatively few Russians have seen Time Machine in the flesh, practically every teen-ager in Moscow owns one of the group's bootlegged tapes.

As have other Western fads, rock music seems to have entered Russia via the Baltic republics and then spread eastward. Some of the best Soviet rock groups, including the Magnetic Band, come from Estonia, which was only incorporated into the Soviet Union after World War II and remains much more Western-oriented than Russia proper.

Even so, Graps was writing songs for himself for six years before getting a chance to appear in public. He admits to being influenced by Western trends, particularly the group Heavy Metal, but insists that he is trying to evolve his own distinct style through his songs, which deal with social themes and relations between people. There are still many people, he says with a smile, who dislike his music.

At one of the concerts given by Magnetic Band in Moscow this month, several people walked out in apparent disgust. The audience was warned beforehand against getting "too emotional" -- and order was maintained by a team of "volunteer" bouncers led by a severe lady called Valentina who ejected several overwrought fans.

In his dressing room afterward, Graps alluded to the pressures every Soviet rock star faces. His dream, he said, was that music should be separated from politics--and judged according to its own merits.

Asked what advice he had for aspiring young singers, he replied: "They shouldn't worry about the obstacles they're bound to run into. They should just do what feels right for them and not give up, and then perhaps they'll succeed."

The manager of another Soviet pop group echoed his feelings. "This is a strange country. At first sight, everything seems impossible. But if you are persistent enough, you can do anything -- even become a rock star."