In Search of Melancholy Baby by Vassily Aksyonov (Random House: $15.95; 229 pp.)

Vassily Aksyonov, whose novel, “The Burn,” is one of the masterpieces of dissident Soviet literature, has been living in this country for the last half-dozen years. He is not really qualified to write about the United States. He is marvelously well qualified to write about himself in the United States.

“In Search of Melancholy Baby” does too much of the first and too little of the second. It takes a long time for an emigre to arrive; particularly, an emigre writer. The flowers are different, Josef Brodsky once pointed out; and more important, the words for the flowers are different.

Aksyonov is getting here, as we can see from the mordant and singularly voiced passages that sprout here and there in these American reflections. He is not here yet, as we see from the rather familiar generalities, sometimes whimsical and sometimes solemn, that threaten to turn his book into a Visitor’s Book.

Or, if you like, he has arrived and unpacked everything but himself. He has still to make himself the metaphor for his America; the kind of thing that Vladimir Nabokov did with his fictional selves in “Lolita” and “Pnin.”

Aksyonov left the Soviet Union in 1980 after the failure of a Russian gamble. (Russian gambles are to gambles as Russian roulette is to roulette.) Along with other leading writers, Lev Kopelev among them, he attempted to challenge the long icing-over of the 1960s thaw by opening the desk-drawers in which Soviet writers were depositing their work and publishing a selection of them under the title of “Metropol”--not secretly but publicly. It was like planting strawberries in January.

Exiled, he crisscrossed the United States, speaking and occupying writer’s residencies at universities all around the country. Finally he settled in Washington as a fellow of the Kennan Institute, and a teacher at Goucher College and Johns Hopkins University in Baltimore.

Aksyonov says fairly predictable things about the fresh and uninscribed minds he finds at Goucher, predominately a college for women. He is taken aback by the students’ ignorance of world history and literature; and moved by their eagerness to be taught. A note of sharpness--one of his literary strengths and used too little in this book--comes when he compares the place to the Smolny Institute for Daughters of the Nobility in Czarist Russia.

Another sharpness, rich in possibilities, is his comment on the institution of the university writer-in-residence. “The writer is as common on American campuses as the cocker spaniel is in American homes,” he writes. A comfortable kind of writer, he implies; and a comfortable kind of dog; lacking in literary and canine bite, respectively.

There are other sharpnesses, here and there. He goes into a left book store in Washington and examines the posters of Stalin, Brezhnev, Mao Tse-tung and Ho Chi Minh. Which, he asks the puzzled proprietor, does he find most attractive “in terms of male beauty?”

That is the astringent Aksyonov of “The Burn.” But much of the book is taken up by the polite Aksyonov of the refugee visa. At one point, in fact, a passing remark places the book’s airiness in a sober context. The writer, who finally gained resident status after much pain and anxiety, lets us know that he is not totally past feeling that being offensive could lead to deportation.

There is not a great deal that is either offensive or particularly stimulating in the author’s observations about motels, supermarkets, landscapes, junk mail, banks, food, the gay rights movement, or cocktail parties. In Washington, he remarks, the weather is humid and people talk about politics all the time.

Although not above noticing that there are rats in his neighborhood’s back alleys, and that it can take forever to get anything fixed, he can be startlingly Pollyannaish. Living in a $1,200-a-month apartment, he speculates that American energies have nowhere to go “now that Capitalism has brought luxury to the millions.”

He calls Bronxville--one of the most expensive New York suburbs--”the real America of neat little towns.” He tells us that taking money from the rich will not remedy economic and social inequality; and that the ideal situation is inequality above an assumed threshold. That assumed threshold consists of everyone having a place to live, food to eat and clothes to wear. It is a lot to assume, even for a recent emigre.

Aksyonov is out of sympathy with the rhetoric and assumptions of the peace movement--understandably, as an exile from a country where the peace movement exists only to protest American missiles. Here too, he is polite, commenting that the United States’ virtue is to allow foolishness as well as sense.

But politeness is not Aksyonov. There is a feeling of discomfort about the book, heightened by an English that is commendable but treacherous. “What has he got against America, that big wig German?” he asks of a critical European intellectual.

He is, as I say, not really here yet. A series of interleaved notes for a future novel about America promises that the author will have something more idiosyncratic to offer. Unfortunately, the notes are jumbled and unclear; a low-energy phase of Aksyonov’s surreal current.

Some of the best passages, in fact, go back to the Soviet Union. A Soviet officer on the Chinese border laments that if war comes, the Chinese will invade and confiscate his new motorcycle. Isn’t he afraid of the Americans as well? Aksyonov asks. No, the major replies, because the United States “respects private property.”

He recalls the Hemingway passion that swept the Russian intelligentsia in the ‘50s and ‘60s. There was the emphasis on the solitary hero, of course; there was also the drinking. Russian culture, Aksyonov reflects, has a periodic need for some new romantic justification of alcohol. “Now Russians could drink with Hemingway in a new American cosmopolitan fashion.”

And he writes of what American jazz meant to his generation: an escape from regimentation and the leaden cult of the socially commendable. One of the friends of his youth, now a general in the Soviet Strategic Air Command, is an impassioned jazz fanatic.

When Aksyonov tells him he is emigrating to the United States and will be able to hear their heroes perform live, the general replies:

“It’s not the same. I don’t go to their concerts when they come. You see, I don’t want them to turn into living people, people like me. It would destroy my world. I need them to be inaccessible. I need their music to come from east of the sun and west of the moon.”

The phrase blazes up in the fissures both of our world and of ourselves. Aksyonov, who once listened to a pirated version of “Melancholy Baby” stamped upon an old X-ray plate, has an artist’s courage, not a general’s. He has not found Melancholy Baby yet; he has taken the risk of never finding it. If he does, it will be in himself, wherever he is, and maybe even in Washington.