Norway and the Soviet Union finished in a dead heat in a dramatic 40-kilometer relay race yesterday in the world Nordic skiing championships in Oslo.

Both teams were awarded gold medals. Finland won the bronze in a photo finish with East Germany.

Oddvar Bra of Norway and Alexander Zavialov of the Soviet Union fought shoulder to shoulder over the last eight kilometers.

About 400 meters from the finish line, Bra tried to pass, there was a scuffle and Zavialov went down. One of Bra's sticks was broken and he skied with only one until a Norwegian coach at the side of the track handed him another

Zavialov recovered and caught Bra as they came to the line. Right at the finish, there was another incident. Bra's left ski went sliding over toward the Soviet and they almost collided again. Bra finished on his back.

The Norwegian considered filing a protest over the first clash, but did not do so. After studying photographs of the bizarre finish, the jury ruled it a dead heat.

Bra previously had won the individual 15-kilometer event, so this was his second gold medal of the championships. A fellow member of the 40-kilometer team, Ove Aunli, set a unique record. He got a gold medal to add to the three already won here by his wife, Berit. A husband and wife had never won golds in the same world championships before. It was Norway's sixth gold of the championships and the Soviet Union's first.

The American team finished eighth. It was without its No. 1 skier, Bill Koch of Putney, Vt., who withdrew because of a viral infection.