A detailed study of GaAs frown directly on offcut (0 0 1) Ge substrates by both solid-source and gas-source molecular beam epitaxy (MBE) has been conducted. It was found that control of As-2 initial exposure and a clean Ge surface were crucial to achieve anti-phase domain-free growth of GaAs on Ge. Under optimized growth conditions device-quality GaAs film was obtained, in which significantly reduced interdiffusion across the GaAs/Ge interface was achieved.