The Soviet Union's supersonic airliner, the TU-144, began scheduled round-trip passenger service yesterday with a two-hour flight between Moscow and Alma Ata in central Asia, 21 months after its Western rival, the Anglo-French Concorde, started regular operation.

The slim white 140-seat plane, which strongly resembles the Concorde, carried a crew of 10 and 80 passengers on the 2,000-mile inaugural flight. Among the passengers, mostly Soviet officials and journalist, were 15 Western reporters.

"It was a good flight without anything unusual," said Captain Boris Kuznetsov after the plane completed the return trip to Moscow.

With "Love Story" blaring from the loudspeakers, Kuznetsov landed at Alma Ata and popped the plane's parachute to assist in braking the plane. On the runway, official speechs linked the new supersonic service with the 60th anniversary of the Russian Revolution, which the Soviets celebrate next week.

Soviet Deputy Civil Aviation Minister Konstantin Gulakov called the flight "a gret achievement, a huge contribution to the celebrations of the 60th anniversary of our great October Socialist Revolution."

The Soviet airlines Aeroflot announced that the Tu-144 would carry passengers on the route once a week. Gulakov declined to say what other regularly scheduled flights the jetliner would make in the future, but it is expected eventually to compete with Concorde on overseas runs.

About 30 of the supersonic airliners are believed to have been produced, at undisclosed cost. Soviet officials talked about exporting the plane in the early 1970s, but a widely publicized crash at the 1973 Paris air show in which 14 persons were killed apparently set back sales ambitions.

The plane's designer said the Soviet Union's current fleet of the Tu-144s has now flown a total of 2.5 million miles.

The Soviet craft reached a speed of 1.430 miles an hour yesterday and flew at a maximum altitude of 55.250 feet. Several reporters aboard the plane said there was considerable cabin noise on the otherwise pleasant flight.

"I was sitting by the window and couldn't talk to the person sitting two seats away on the aisle," one correspondent said. "I had to communicate with him by notes." Another passenger reported problems with the toilet and water equipment, but said they appeared routine for a new airliner.

The reading lights did not work, and there was no in-flight entertainment, but passengers were served a breakfast of caviar, roast beef, wine and cognac high above the Russian steppes.

As on the 126-seat Concorde, the arrangement of the 140 powder-blue seats on the TU-144 makes for a cramped flight. In the front half of the plane, there are three seats on one side of the aisle and two on the other, while in the narrow rear part of the fuselage seating is two by two .

One-way fare for the regular Moscow-to-Alma Ata flight is still $111 - or about 5.5 cents per mile. The Concorde's fare between London and Washington is $884, or about 53 cents a mile.

The Soviet fare is about 17 per cent higher than the normal fare between the two points for flights that usually take at least four hours and 20 minutes.

The plane's chief designer, Alexei Tupolev, whose father Andrei designed the first Soviet jet, was aboard and acknowledged the noise problem, saying it was inevitable with supersonic flight.

"The sonic boom is no different that a thunderclap - so it is no different than nature itself," he said.

Tupolev said the high noise level was caused by the plane's powerful engines and by an air ventilation system needed to cool the 248-degree temperatures on the plane's titanium body.

"We are looking into the problem," he said. "We need very strong ventilation with lots of air moving."

Outside noise at takeoff from Moscow reportedly reached 110 decibels, compared to 105 decibels measured during the first tests of the Concorde last month at New York's John F. Kennedy airport.

Tupolev said theplane is only a few decibels higher than the subsonic Tu-154 and lower than the Tu-104 the first subsonic jet craft used in Soviet commercial aviation.

The Tu-144 was once expected to enter passenger service as early as 1973, but a series of setbacks - the worst being the crash at the 1973 Paris air - delayed the start of regular flights.

An improved prototype was sent to the 1975 show but it reportedly had to make an emergency landing in Poland on its way home because of mechanical problems.

The aircraft began regular freight and mail flights between Moscow and Alma Ata in December, 1975, while technicians continued to work on problems including high fuel consumption, shortened range, vibrations and sonic booms.

The Soviets have set and broken various dates for the start of regular passenger service. The firmest date ever given by the Ministry of Civil Aviation was mid-1975, but it came and went with no passenger service and no explantion.

The plane has undergone two extensive modifications since the 1973 crash, apparently to increase stability at lower speeds, according to some Western observers. The Tu-144's rated range is 4,000 miles and its ceiling about 6,000 feet.

The Concorde, which can reach 1,350 miles per hour, has a 3,300-3,800 mile range and a ceiling of about 6,000 feet.

Pilot Kuznetsov's crew included a co-pilot, navigator, engineer, three hostesses and three stewards for yesterday's flight. The stewardesses apparently had a new uniform designed for the occasion, with blue and white tunics and a silk scarf around the neck.