Launch from the Baikonur Cosmodrome. Following a two day solo flight Soyuz TM-21 docked with the MIR space station on March 16, 1995. Norman Thagard became the first American astronaut to launch on a Soyuz spacecraft and board MIR.

The resident crew was exchanged. The three cosmonauts became the 18th resident crew. Norman Thagard became the first U.S. astronaut onboard the MIR space station. On June 02, 1995 the new Spektr module docked with the MIR.

Vladimir Dezhurov and Gennadi Strekalov performed five EVAs on May 12, 1995 (6h 14m), May 17, 1995 (6h 41m), May 22, 1995 (5h 14m), May 28, 1995 (0h 21m) and June 01, 1995 (0h 22m) to rebuild the space station (installation of solar array and repositioning docking adapter). There have been several technical problems during this mission. The cosmonauts also performed life science experiments.

The crew members were relieved by Space Shuttle Atlantis during STS-71, when they were replaced by expedition MIR-19, who returned to earth aboard Soyuz TM-21 on September 11, 1995.