The two Russians and Frenchman Jean-Pierre Haignere, who remained on board during the spacewalk, are expected to return to Earth on August 28.
Mir will continue to orbit unmanned for several months afterwards as space officials make one final effort to support a station the government says it can no longer afford.
If new funds are not found Russia will probably bring down Mir in early 2000. This would be about the same time as the first crew is scheduled to begin living on the new International Space Station, in which Russia, the United States, Europe, Japan and Canada are involved.
Mission Control spokeswoman Vera Medvedkova said the cosmonauts were not scheduled to look for the source of a pressure leak detected in late June.
Officials have said the slow leak could make the station uninhabitable after three months.
Flight engineer Avdeyev -- the world's most experienced spaceman with a cumulative time of 717 days in space -- was making a spacewalk for his eighth time, and Afanasyev for his seventh.
Russian cosmonaut Anatoly Solovyov holds the record with 15 spacewalks.