Mir and ISS were up at the same time, but not manned at the same time. The last mission to Mir, Soyuz TM-30, came home on June 16, 2000, and Expedition 1 to the

Mir and ISS were up at the same time, but not manned at the same time. The last mission to Mir, Soyuz TM-30, came home on June 16, 2000, and Expedition 1 to the ISS launched on November 1st, 2000. The first component of the ISS, the Zarya, was launched in November 1998, and the Mir deorbited March 23, 2001, so for that time there were two stations in space, but never manned at the same time.