We report the first study of single‐crystalline GaAs grown by molecular beam epitaxy (MBE) on a nonpolar substrate. In this study, GaAs was grown under various conditions on Ge(100). Surface morphologies were specular and quite strongly dependent on surface preparation. Photoluminescence spectra from such GaAs is quite intense and is dominated by donor–acceptor recombination at 1.479 eV which appears to be Ge0Ga−Ge0As. We also observe its phonon replica at 1.442 eV and the recombination of bound excitons at 1.514 eV. This and capacitance–voltage measurements indicate incorporation of Ge from the substrate into the GaAs. Photoluminescence from GaAs/AlGaAs multiple quantum well structures originates from the same processes as in bulk GaAs; in quantum wells, however, the transitions occur at higher energies due to the enhancement of the GaAs band gap. The observed energies are in good agreement with theoretical predictions. We have also studied the growth of GaAs on Si(100) and on Ge films on Si(100).