A Monte Carlo simulation method in the canonical and in the grand canonical ensembles is used to study the behavior and properties of dense monolayer and bilayer films formed on the (100) plane of model face-centered cubic crystals. Systems with different effects due to the periodicity of the gas-solid potential are considered, and the mechanism of melting in the first and the second adsorbed layer is discussed. It is demonstrated that the film structure is very sensitive to the gas-solid potential corrugation, as well as to the temperature and the surface coverage. In particular, it is shown that monolayer films formed on weakly corrugated surfaces exhibit the incommensurate (dense) phase at sufficiently low temperatures, and the two-dimensional liquid phase of lower density, when the temperature: is higher than a certain transition temperature, which depends on the surface corrugation. In the case of intermediate corrugation, the incommensurate solid coexists with the registered (1 x 1) phase, while for highly corrugated surfaces only the registered monolayers are stable. It is also shown that the melting temperature for the first layer is very sensitive to the surface corrugation, while in the second layer we do not observe such strong effects.