Vasili Aksyonov, one of the Soviet Union's most popular novelists and screenwriters, today left Moscow to live in America, ending years of censorship tussles and escaping the total ban that has been slapped on his works here.

The 47-year-old writer, with his wife, Maya, and three other family members, flew to Paris this afternoon to travel and live aboard on two-year Soviet exit visas. He plans to settle in the United States and has invitations to teach and work from several universities.

Aksyonov's departure achieves much for Soviet authorities, who long have been eager to ensure his silence here while avoiding the kind of Western criticism that internal exile or a political trial would trigger. A member of the so-called "fourth generation" of new Soviet writers who emerged to stir up the Moscow literary world during the Khrushchev thaw of the early 1960s, Aksyonov has been a particular target of the authorities for the past two years.

They were outraged when he organized a group of 25 other writers and artists to produce a collection of their work, "Metropol," early last year and demand it be officially published without state censorship.

In a bitter sequence of denunciations and reprisals, the official writers' union barred two young "Metropol" members from the union, Aksyonov resigned in protest, and in turn was ex- pelled from all other official literary groups, virtually shutting the door for good on any chance he would be published here ever again.

Other prominent Moscow writers who participated in "Metropol," such as poet Bella Akhmadulina, and fiction writer Fasil Iskandr, have also been under a acloud since the "Metropol" affair, which state literary officials have labeled an anti-Soviet plot designed to denigrate Soviet literature. The collection, which included specific sexual references and scatological words never allowed by the censors, has been called "trash" by the writers' union apparat.

The authorities' anger at Aksyonov increased this spring when a smuggled copy of his newest novel -- which Moscow intellectuals who have read it call his best -- appeared to rave reviews in Italy.It is now a best seller there, an Houghton-Mifflin Co. plans to publish the book in the U.S. It's Russian title is "The Burn," a semi-autobiographical account of the psychological distortions and tensions created by life in a totalitarian state.

Aksyonov's wife is Maya Karmen, widow of the Soviet Union's most famous find documentarian, Roman Karmen, who was co-producer with Isaac Keinerman two years ago of the Soviet-American documentary series on "The Unknown War," about World War II as fought by the Russians. Highly praised here, the series received sharp criticism in the United States.

The aksyonovs were accompanied by their daughter, Yelena Grinbers, son-in-law, Vitali, and their child, an 8-year-old boy. The Grinbers intend to settle permanently in the United States, but Aksyonov says he intends to return to the Soviet Union at the Expiration of his visa.

Like so many Soviet intelligentsia, Aksyonov's entire life has been tangled with officical oppression. When he was 4, his parents disappeared into the Gulag, victims of the Stalinist purges. When they reappeared 18 years later, the son already was grown and studying medicine, but burning to write of the gritty life of his own generation.

When "Starry Ticket," an early novel, appeared, its exotic slang and tales of street-wise young Moscovities smitten with Western styles and aimless adventures that shocked their elders won him instant fame. But a few years later, Khrushchev himself was denouncing Aksyonov in a famous Kremlin shouting match in 1963. "I know you," he bellowed. "You're trying to avenge your father."

Aksyonov's career has been marked by the same cycles of official acceptance and repression that have dogged most of the best writers here since then. But in recent years, as the conservative leadership has clamped down on all stray and dissenting voices, the writers have come under increased pressure. Many of them find the struggle to overcome censorship and timid editors not worth the effort; the "write for the desk," a traditional Russian practice, or manage to get their manuscripts out to the West.

The "Metropol" collection has been published in a Russian language edition by Ardis Press of Ann Arbor, Mich., and W. W. Norton & Co. of New York plans an English edition.

The family's baggage was subjected to minut scrutiny today by customs agent at Moscow's gleaming new Sheremetyevo-2 Airport, an exact copy of the Hanover Airport and built by the West Germans to help the Soviets dazzle visitors to the Olympic Games. Seven customs agents labored for 90 minutes over the bags, reading manuscripts, pawing through the women's extra undergarments and finally refusing to allow them to take any extra jewelry and other mementos.

Articles rejected to customs included all of Aksyonov's wife's personal documents, including their marriage certificate, her graduation diploma, her late husband's death certificate and a cheap tin tray, available for 10 rubles in any Moscow store. "Real Russian handicrafts," ruled the agents.