Anatase (TiO2) films have been grown by oxygen plasma assisted molecular beam epitaxy. Reflection high-energy electron diffraction and low energy electron diffraction indicate that the films grow epitaxially with respect to the substrate. For (001) anatase films grown on SrTiO3 (001) we have found that a (1 X 4) reconstruction is formed under growth conditions. On cooling to room temperature this reconstruction remains. The (101) anatase films were grown on a natural anatase (101) substrate. The natural substrate (i.e., mineral) was used due to the difficulty in obtaining good lattice matched materials for this surface orientation. X-Ray photoelectron spectroscopy results indicate that both surfaces are fully oxidized with Ti in the 4+ oxidation state.