Launch from the Baikonur Cosmodrome; landing with Soyuz 37 capsule 140 km southeast of Dzheskasgan.

Following a one day solo flight Soyuz 35 docked with Salyut 6 on April 10, 1980. The cosmonauts became the fourth resident crew. Valeri Ryumin was not originally planned for this mission, but Valentin Lebedev was injured on his knee before the launch and had to be replaced by Valeri Ryumin.

The dockings of Soyuz 36 on May 27, 1980, of the new developed spacecraft Soyuz T-2 on June 05, 1989, Soyuz 37 on July 24, 1980 and Soyuz 38 on September 19, 1980 brought visiting crews to the station. Supplies were brought with cargo spacecrafts Progress 8 - 11. The space station was in good, but not in perfect shape, when the crew arrived. Two viewports in the transfer compartment had lost their transparency.

The cosmonauts had a rather busy time onboard the station. They replaced components of the attitude control system and life support system, installed a new caution and warning system, synchronised the station's clocks with those in the TsUP, added an 80 kg storage battery, and replaced air from tanks in Progress 8.

By April 15, 1980, the Progress tanker had been emptied of supplies, and the crew filled it with garbage and deorbited the craft April 25, 1980. Two days later, Progress 9 was launched, docking with the facility on April 29, 1980. The next day, the first-ever transfer of water between a tanker and a Salyut station was completed. Cargo transfers and refuelling operations were completed by May 12, 1980. With this flight, the resupply of the Salyut was complete for the long-duration crew.

Several scientific experiments were performed as biological cultivation tests, photography of the Earth surface, materials science Kristall or Splav-01 materials processing furnaces. Minor repair work was carried out by the crew and "Lotos" was carried out, an experiment involving using special moulds to make plastic items with a quick-setting material. Additional experiments involved production of polyurethane foam, exploring its utility in assembling structures in orbit.

Progress 9 was undocked May 20, 1980, leaving the rear port vacant for the arrival of the next crew. Soyuz 36 was launched May 26, 1980. Valeri Kubasov and Bertalan Farkas swapped Soyuz craft with the long-duration crew, departing the station in Soyuz 35 on June 03, 1980. The next day, Leonid Popov and Valeri Ryumin entered Soyuz 36, undocked it from the station, then redocked it 90 minutes later at the vacant front dock. 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. A launch indeed was soon in the offing, but not the predicted mission.

The resident crew carried out repairs of the station's Kaskad attitude control system and performed materials processing experiments. On July 01, 1980, Leonid Popov and Valeri Ryumin received Progress 10 at the station. Replacement equipment was unloaded from the supply tanker, as were regular crew supplies. Supplies included a Polaroid camera, a color television monitor, and tapes of Soviet pop music. The tanker was undocked from the complex on July 17, 1980 after refuelling the station and deorbited July 19, 1980. Also on July 19, 1980, Leonid Popov and Valeri Ryumin sent their greetings from the station to the 1980 Summer Olympics, wishing the athletes happy starts in a live communication between the station and the Central Lenin Stadium where the opening ceremony was held. They appeared on the stadium's scoreboard and their voices were translated via loud speakers.

The crew set a new spaceflight record.