The growth dynamics of GaAs, AlAs and (AI, Ga)As films grown by molecular beam epitaxy (MBE) on GaAs (11 0) and (1 11)Asubstrates have been studied using reflection high energy electron diffraction (RHEED) intensity oscillations and scanning tunnelling microscopy (STM). In contrast to growth on (0 01) oriented substrates, the period of the RHEED intensity oscillation does not in general provide a measure of the growth rate. This is explained bythe very different surface chemistry involved, since the short lifetime of arsenic molecules (As= or As4) on non-(001) surfaces results in cation-stable surface conditions, which generate arsenic (anion)-induced intensity oscillations, whereas on (0 01) surfaces they are cationinduced under all normal growth conditions. The effects of this behaviour on surface morphology are illustrated, as are the relative influences of Ga and AI. STM images obtained during the first few monolayers of growth provide a detailed indication of the growth mode and in particular explain in a simple manner the origin of bilayer period RHEED intensity oscillations obtained during growth on GaAs (110).