Soyuz TM-27 carried the Mir EO-25 crew and French astronaut Leopold Eyharts. NASA and the Russian Space Agency had hoped Soyuz TM-27 could dock with Mir while Endeavour was still there, resulting in an on-board crew of 13, a record which would have stood for years or decades. But the French vetoed this, saying the commotion and time wasted would ruin Eyharts Pegase experimental programme. Soyuz TM-27 docked at the Kvant module port at 17:54 GMT on January 31, 1998, less than five hours before Endeavour landed in Florida.

Solovyov handed over command of Mir to EO-25 commander Musabayev, and the Mir EO-24 crew and Eyharts undocked from the forward port of Mir at 05:52 GMT on February 19 aboard the Soyuz TM-26 for their return home. On February 20, the EO-25 crew and Andy Thomas of the NASA-7 mission boarded Soyuz TM-27 and undocked from the Kvant port at 08:48 GMT. They redocked with the forward port on Mir at 09:32 GMT. This freed up the Kvant port for a test redocking of the Progress M-37 cargo ship, parked in a following orbit with Mir during the crew transfer.

Soyuz TM-27 undocked from Mir at 02:05 GMT on August 25, with Musabayev, Budarin and Baturin aboard. They landed on August 25 at 05:23 UTC near Arkalyk in Kazakstan.