Soyuz 35 was launched 9 April 1980 with Leonid Popov and Valery Ryumin aboard for a planned rendezvous with the orbiting Salyut 6 space station.

[2] Valentin Lebedev had been scheduled to be Popov's flight engineer, but he was disqualified from launch after suffering a knee injury in a trampoline accident.

Additional experiments involved production of polyurethane foam, exploring its utility in assembling structures in orbit.

[3] The launch was a part of the Soviet Intercosmos program whereby guest cosmonauts from allied nations would visit the space station, typically for about a week.

[2] The rapid switch of ferry vehicles, along with the launch of Soyuz 36 at almost the earliest possible date to allow a crew recovery in the nominal window, caused observers to speculate the secretive Soviets were possibly planning a second Intercosmos mission to recoup the time lost after the Soyuz 33 failure.

[2][3] The resident crew carried out repairs of the station's Kaskad attitude control system and performed materials processing experiments.

Supplies included a Polaroid camera, a color television monitor, and tapes of Soviet pop music.

[2] The launch was timed to take advantage of the world's focus on the Soviet Union during the Olympic games.

Pham Tuan's flight also had political implications as he was a decorated flying ace from the Vietnam War and had shot down several American aircraft, a fact that the Soviet media readily pointed out.

The mission was interpreted as a subtle means of retaliation against the United States for boycotting the Olympics.

The following day, Popov and Ryumin boarded Soyuz 37 and redocked it to the front port, suggesting to observers that another crew's launch was coming shortly.

[2] The launch, therefore, of Progress 11 on 28 September came as surprise to observers, as it was assumed cosmonauts due to return to Earth would not need fresh supplies.

In fact the real purpose of Progress 11 was to boost Salyut 6 into a higher orbit during the six months between crew residencies, since its defective propulsion system could no longer be used.

The fourth Salyut 6 residency was at last a complete success after the numerous technical malfunctions that dogged the first three crews.