Abstract RHEED intensity oscillations in the process of MBE growth of Ge and Si on Si (100) and Si (111) substrates were observed. It is revealed that a finite-thick buffer layer can improve the surface flatness of Si substrates, and the employment of lower growth rate or growth interruption procedure can improve tke crystal quality of epilayers. During the growth of Ge and Si on Si (100), a single atomic layer mode RHEED intensity oscillation was observed along either  or  azimuthal direction, which is due to the existance of double domain (2×1)+(1×2) reconstruction on the surface. During the growth of Ge on Si (111) substrates, RHEED intensity oscillation show a bilayer mode observed along  azimuth, but a non-uniform periodicity along  azimuth. The oscillations for continuosly growing Ge-on either Si (100) or Si (111) could exist up to an epilayer thickness of 6ML, which corresponds to the critical thickness of pseudomorphic growth of Ge on Si.