Metamorphic high electron mobility transistor (M-HEMT) structures have been grown on GaAs substrates by molecular beam epitaxy (MBE). Linearly graded and the step-graded InGaAs and InAlAs buffet layers hal e been compared, and TEM, PL and low-temperature Hall have been used to analyze the properties of the buffer layers and the M-HEMT structure. For a single-delta-doped M-HEMT structure with an In0.53Ga0.47As channel layer and a 0.8 mum step-graded InAlAs buffer layer, room-temperature mobility of 9000 cm(2)/V s and a sheet electron density as high as 3.6 x 10(12)/cm(2) are obtained. These results are nearly equivalent to those obtained for the same structure grown on an InP substrate. A basic M-HEMT device with 1 mum gate was fabricated, and g(m) is larger than 400 mS/mm.