Three GaSb single crystals have been successfully grown under microgravity on Spacehab-4 during the STS-77 Space Shuttle flight. Two Te-doped crystals with 16 mm diameter and lengths of 31.5 and 18 mm, respectively, were grown by the floating-zone method. From the transition of striated to striation-free material it was possible to determine the critical Marangoni number for the onset of time-dependent thermocapillary convection for the FZ growth: Ma c2=375±125. This is in good agreement with 3-D numerical simulations resulting in Ma c2=355±90. The simulations showed that the 3D flow pattern with an azimuthal instability varies from Si-FZ configurations; the reason is most probably the more barrel-shaped zone caused by the large growth angle of 30.7°. In addition to the FZ crystals, one undoped crystal with 15 mm diameter and 1 mm crystallized length was grown from a free Bi zone, the first time a crystal was grown from a free solution zone in space. On earth, a free Bi solution zone is not only limited to small diameters as in the FZ method, but cannot be used at all due to fluid creep. Under μ g, the Bi zone was stable and the grown crystal is free of cracks.