Using Monte Carlo simulation methods in the canonical and grand canonical ensembles, we study the melting and the structure of low-temperature phases of mixed Ar–Kr submonolayer films on graphite. It is shown that such films exhibit a complete mixing in the liquid phase and freeze into a mixed solid phase, independently of the composition. The structure of the solid phase, however, depends upon the film composition, its total density, and the temperature. For submonolayer coverages, when the mole fraction of Kr is lower than about 0.1, the mixture freezes into the incommensurate, argon-like phase. For the higher mole fractions of Kr, the freezing leads to the formation of a mixed commensurate (√3 × √3)R30° phase. The lowering of temperature leads to structural phase transitions in the solid. When the krypton mole fraction is lower than about 0.88, the transition leads to the formation of domain-wall structures, in which the commensurate domains are made of krypton atoms, while the composition of walls depends upon the Kr mole fraction. It is shown that even rather small concentrations of argon atoms can trigger the commensurate–incommensurate transition. For still higher Kr mole fractions, exceeding about 0.88, the commensurate, krypton-like, solid phase is stable at any temperatures below the melting point. At sufficiently low temperatures, the phase separation takes place and argon atoms are removed from the film interior to the peripheries of submonolayer. In the case of films with the total density close to the monolayer completion, the commensurate structure shows much higher stability. It is demonstrated, however, that it is an artifact of the simulation methods used and, in particular, of the periodic boundary conditions applied, rather than a real phenomenon. It is also demonstrated that the phase diagram topology of monolayer films changes with the film composition. In particular, the vapor–liquid critical point appears only when krypton concentration is lower than about 0.45.