We report on the growth by molecular beam epitaxy of high‐quality GaAs and AlxGa1−xAs (x≲0.43), and discuss the effect of system parameters on material quality. The highest Hall mobility in GaAs at 77 °K was 144 000 cm2/V sec, and the photoluminescence spectra of undoped layers exhibited a strong free exciton line and a much reduced carbon peak with no carbon‐related defects. A slow growth process at a substrate temperature of 600 °C produced excellent AlxGa1−xAs whose luminescence spectrum showed a distinct excition peak 4 meV wide. This AlxGa1−xAs is compared to layers grown at a faster rate at substrate temperatures of 700 °C.