Self-diffusion in single crystal InP and GaAs has been measured, together with the diffusion of the acceptors Cd and Zn and the donors S and Se in GaAs. Radioactive isotopes of these elements were used as tracers. The diffusions of In and P in InP are characterized by activation energies of 3.85 ev and 5.65 ev, respectively; those for Ga and As in GaAs are characterized by activation energies of 5.60 ev and 10.2 ev, respectively. The marked differences in both activation energies and diffusion rates of the constituent atoms in these materials indicate that the basic mechanism of the self-diffusion is one of migration within a specific sublattice. The impurity diffusion measurements in GaAs suggest that the concept of sublattice diffusion be extended to include impurity diffusion when the impurities enter the lattice substitutionally. The activation energy of the diffusion of both Cd and Zn in GaAs is about 2.5 ev, while that of the diffusion of both S and Se in GaAs is about 4.1 ev. Experimental details of interest include the observation of GaS compound formation when GaAs is heated in S vapor, and the formation of glassy layers on the surface of GaAs due to Se.