Soyuz 31, the third Intercosmos flight, was launched 26 August 1978. Cosmonauts Bykovsky and Jähn were greeted by resident crew Vladimir Kovalyonok and Aleksandr Ivanchenkov when they docked at the aft port of the Salyut 6 space station the next day. The visitors brought with them fresh onions, garlic, lemons, apples and other food for the long-duration crew, then in space for more than two months.

The presence of the East German cosmonaut was seen as significant because of the presence of the MKF-6M camera on the space station, built by the Carl Zeiss works at Jena. Medical and biological experiments were carried out, including an audio experiment which tested sound and noise perception limits. An experiment called Berolina used the Splav furnace to process an ampoule of bismuth and antimonide with the material between two plates in the ampoule. The tree structure which resulted was four to six times larger than what had been produced on the ground. Another experiment tested using different photographic films on the station's interior.

The Soyuz 31 crew swapped craft with the Soyuz 29 crew so as to supply the long-duration crew with a fresh craft. On September 2, the engines of Soyuz 29 were tested, 25 experiment containers with 100 experimental results were transferred, along with exposed film, and seat liners and centering weights were exchanged. The Soyuz 31 crew left in Soyuz 29 the next day and landed 140 km southeast of Dzhezkazgan.

The standard recovery procedure was changed with this flight, observers noted. In the past, the recovery of a civilian Salyut crew had been made on the orbit following the one which provided a nominal launch opportunity to Salyut. With this and subsequent flights, the landing occurred during the orbit which provided the nominal launch opportunity. The effect of this change was to have a landing window open some two to three days earlier than otherwise.

The crew on the station subsequently boarded the Soyuz 31 vehicle and redocked it to the forward port, thus freeing the aft port for a forthcoming Progress supply ship. They returned to Earth 2 November in the craft after setting a new space-endurance record of 139 days.