The initial stages of the deposition of thin zinc films on the (110) and (100) surfaces of germanium single crystals have been studied. A mass-spectrometric molecular beam method was used in ultrahigh vacuum. The evaporation rate of the thin film was measured during depositions at various temperatures and beam intensities. On both substrates, the adcoverage approaches complete saturation of available adsorption sites before nucleation of bulk zinc starts. Nucleation therefore occurs on a composite substrate. On (110) substrates, the critical nucleation stage of thin film formation is determined by the coverage only. The thermodynamic parameters of the critical deposit, such as the equilibrium evaporation rate, the thermodynamic potential, and the differential binding energy, have been determined. These thermodynamic parameters determine the critical beam intensity necessary for nucleation. The deposition of zinc on (100) substrates is more complex. The critical nucleation state of the deposit is determined not solely by the coverage, but also by the deposition conditions of temperature and beam intensity. In such a case, thermodynamic parameters cannot be obtained by the present technique.