Studies of intensity oscillations of the specularly reflected reflection high-energy electron-diffraction (RHEED) beam during the growth of YBa2Cu3O7-x and DyBa2Cu3O7-x thin films on (100)SrTiO3 substrates are presented. These studies have been conducted under controlled conditions of atomic fluxes, substrate temperatures, and oxygen partial pressures. The periods of the oscillations have been observed to increase when the substrate vicinal angle is increased, at fixed flux. Oscillation amplitudes have been found to depend on the substrate temperature. The oscillation time periods as well as amplitudes for the Dy and Y compounds have been found to be dramatically different. These observations have been characterized within the framework of a model of RHEED oscillations, which attributes them to changing surface step densities and distributions. After appropriate normalization, the time dependences of the RHEED oscillations obtained at different temperatures coincide for each compound. This indicates that these oscillations are a consequence of surface steps. Such an interpretation yields qualitatively accurate predictions of observed intensity oscillation profiles and is also consistent with transmission-electron-microscope (TEM) studies of nucleation and growth. Bare substrate areas have been found in TEM studies in films which, during growth, exhibited 12 periods of RHEED intensity oscillations. Discrepancies have been found in the thicknesses of films as measured by RHEED oscillations and Rutherford backscattering. These results indicate that assertions of superconductivity in single unit-cell thick layers based on the observation of RHEED oscillations are open to question.