Soyuz 35 was the eighth mission to visit the Salyut 6 space station and carried the EO-4 expedition, which was the fourth long-duration crew for the station. The mission began on April 9, 1980, 13:38:22 UTC, launching Commander Leonid Popov and Research Cosmonaut/Flight Engineer Valery Ryumin into orbit. They docked with the station the next day. During their 186-day stay on the station, EO-4 crew conducted various scientific experiments, some repairs and replacements to the station and were visited by three uncrewed Progress cargo spacecrafts and 4 crewed Soyuz vehicles. Soyuz 35 swapped vehicles with the Soyuz 37 crew, which allowed for a longer stay in orbit.
The mission concluded with a safe landing back on Earth on October 11, 1980, 09:49:57 UTC.