The epitaxial growth of iron oxide films on Pt(lll) substrates was investigated by scanning tunneling microscopy and low-energy electron diffraction. The film growth was accomplished by repeated cycles of iron deposition and subsequent oxidation at p(O-2)= 10(-6) mbar. For oxidation temperatures of 870 K second and third FeO(lll) layers grow layer by layer, whereas for oxidation temperatures of 1000 K only one FeO(lll) monolayer is formed. On top of the FeO(lll) films a homogeneous nucleation of Fe3O4(111) islands takes place, resulting in a Stranski-Krastanov growth for iron oxides on Pt(lll). The islands grow in the Fe3O4 bulk structure laterally much faster than vertically, forming hat platelets with heights up to 100 Angstrom and hexagonal and triangular basal planes 1000-5000 Angstrom in diameter. The islands only expose low index ((1) over bar 11) and {2 (1) over bar (1) over bar} facet planes, and their growth can be described by an Ostwald ripening mechanism that takes place during each oxidation cycle. Eventually the islands coalesce and form smooth Fe3O4(111) films at least 150 Angstrom thick. The atomic and mesoscopic surface roughness bf these films depends on the growth temperature, where the latter ranges between 40 and 100 Angstrom on a length scale of mu m. By a high-pressure oxidation at p(O-2) = 10(-1) mbar the Fe3O4(111) films were transformed into well-ordered alpha-Fe2O3(0001) films with similar surface morphologies. In all oxide phases formed the hexagonal oxygen (Ill)planes are aligned to the Pt(111) substrate surface lattice. The film growth is discussed in terms of surface and interfacial energies, oxidation and growth kinetics, as well as thermodynamic stability ranges of the: different oxide phases. [S0163-1829(99)11007-5].