Aleksei Stanislavovich Yeliseyev (cyrillic Алексей Станиславович Елисеев) was born July 13, 1934 in the city of Zhizdra, Russia. He attended the Bauman Higher Technical School in Moscow, before entering work at Sergei Korolev's design bureau. It was from here that he became selected as a cosmonaut during the 1966 intake of civilian engineers.

His first assignment was one of the crew members on the original Soyuz 2 mission. He was to be one of the two crew members to transfer from Soyuz 2 to Soyuz 1 during the maiden flights of the Soyuz spacecraft. But after rain at Baikonur and problems that Soyuz 1 faced in orbit, the mission was aborted before it launched.

His first flight was a flight engineer on the Soyuz 5 flight. Also on board Soyuz 5 were Boris Volynov and Yevgeni Khrunov. Yeliseyev and Khrunov performed an EVA and transfered to Soyuz 4 were they reentered with Vladimir Shatalov.

He was then assigned as crew member for Soyuz 8 which was part of three spacecraft mission launched October 13, 1969. Soyuz 6 was to have taken spectacular motion pictures of Soyuz 7/8 docking but failure of rendezvous electronics in all three craft due to new helium pressurization integrity test prior to mission did not permit successful rendezvous and dockings.

He was proposed as the a member of the prime crew for a Soyuz test flight of the Kontakt system designed for the lunar orbit rendezvous and docking of the LOK lunar orbiter and LK lunar lander. The system was to be mounted on two Soyuz and tested in Earth orbit.

Yeliseyev last flight was Soyuz 10 launched April 23, 1971. This was meant to be the first space station flight, docking with Salyut 1. It was manually docked after faillure of the automatic system, but hard docking could not be achieved because of the angle of approach. It was realised after the flight that the crew did not have the necessary equipment to assertain their range and angle for a successful manual docking. Soyuz 10 was connected to the station for 5 hours and 30 minutes. They were forced to reenter and during the landing, the Soyuz air supply became toxic. The crew survived but Nikolai Rukavishnikov did become unconscious during the descent through the atmosphere.

In all Yeliseyev spent 8 days, 22 hours and 19 minutes in space.

Following his retirement from the space programme in 1985, he took up at an administrative position at the Bauman school for several years before retiring fully.