InSb and InAs1-xSbx epitaxial layers have been successfully grown on (100)GaAs substrates by molecular beam epitaxy. Remarkably good morphologies were obtained despite the large lattice mismatch (14%) between InSb and GaAs. Room-temperature electron mobilities as high as 57 000 cm2/V s were measured in InSb layers of about 5 μm thick with ND-NA∼1.6×1016 cm-3. The substrate temperature and Sb/In flux ratio were found to critically influence the quality of InSb epilayers. By employing dimeric instead of tetrameric sources, the composition of the InAs1-xSbx films was observed to be relatively independent of substrate temperature. Electron mobilities of 20 000 and 8800 cm2/V s, at 300 and 77 K, respectively, were obtained for a 1.6-μm-thick InAs1-xSbx (x=0.67) layer.