The Soviet Union launched a spacecraft carrying a Russian and a Czechoslovak cosmonaut last night. It was the first time a space flight has included anyone from a country other than the United States or Soviet Union.

Capt. Vladimir Remek, a 20-year old Czechoslovak Communist Party member and military pilot, rode into space from the Baikonur spaceport in central Asia as "cosmonaut-researcher" of Soyuz 28, commanded by a veteran Soviet Cosmonaut, Col. Alexei Gubarev.

The spacecraft headed for rendezvous and docking today with Salyut-6, the 19-ton Soviet space station that already has been the site for two other historic space firsts and whose crew is within little more than one day of breaking the three-year-old U.S. manned space record of 84 continuous days in space.

Remek and Gubarev are scheduled to join the Salyut-6 "for a few days," and then return to earth, according to Tass, the official Soviet news agency.

The successful launching brings yet another space first to the Soviet Union, which began the space age in 1957 with the orbiting of Sputnik 1. The Soviets went on to become the first nation to orbit a live animal, a dog; the first to orbit a human, Yurl Gagarin, in April 1961; and the first to orbit a woman, Valentina Tereshkova, in 1963.

In addition, the Salyut 6 space station itself has established new space firsts: a double docking of two spacecraft with a space station; the first "shuttle" service of a second two-man crew in January for a five-day visit; and the first docking of an unmanned cargo ship, the progress 1 with a manned orbiting spacelab.

The two space station crew members, Yuri Romanenko and Georgi Grechko, achieved the first transfer in space last month of dangerous rocket fuels and oxidizers, successfully pumping them from the cargo ship into the space station to prolong its useful life. This was a major step toward the Soviet goal of assembling and manning large orbital stations for months at a time.

The long-expected Soviet launching of a non-Soviet came as the American space program is in a pause while awaiting perfection for manned orbital flight of the massive space shuttle. The U.S. astronaut program has plans to launch a European crewmenber -- and perhaps a woman -- no earlier than the next decade.

Remek, the son of a deputy defense minister in Czechoslovakia, was one of six prospective cosmonauts of a "first unit" of trainees from Czechoslovakia, East Germany and Poland. The six have been training at the spaceport and Star City cosmonaut training center just outside Moscow for the chance to be the first representative of a third country to orbit the earth.

Vladimir Shatalov, chief of cosmonaut training and a former spaceman, said the choice of Remek over the other five "has not been an easy one. . . The level of training was practically the same."

A Czechoslovak delegation headed by Josef Lenart, a member of the Communist Party's ruling presidium, witnessed the launching.

Soviet television showed the Czechoslovaks and Soviets embracing and smiling with delight as the rocket and spacecraft roared skyward on a tall column of smoke and fire.

The Soviets have used the same adaptation of an early intercontinental ballistics missile, the SS-6, as the mainstay of their orbital space program since the launch of Sputnik 1.

Gubarev, 47, spent 30 days in space in 1975 as commander of the Soyuz 17 spacecraft and Salyut 4, a predecessor of the current orbiting spacelab.

In remarks televised from within the capsule as the two waited to depart, Remek said he was "honored to be a member of an international space crew. I take pride in the fact that my country, just as other countries of the socialist community, are taking an active part in cooperation with the Soviet Union in the exploration and use of outer space for peaceful purposes."

He added "heartfelt thanks" to the Communist leadership of both countries.

Remek was born in Ceske-Budejovice Sept. 26, 1948. He studied piloting in the Soviet Union after becoming a lieutenant in his country's air force, and in 1976 he was chosen as a candidate for the manned space program under the Intercosmos program of space cooperation among the Soviet bloc countries. He began a "full course" of space flight training in December 1976, according to Tass.

The launch of the Czechoslovak comes almost 10 years after the Soviet-led invasion of Czechoslovakia in August 1968 crushed the liberalminded Communist rule of Alexandria Dubcek.

At that time, according to a brief biography supplied by Tass, Remek was enrolled in an air school and that same year became a member of the Communist Party.