The epitaxial growth of MoO2 crystallites on a Mo(110) surface has been studied by RHEED. The Mo surface was heated at 850-degrees-C in an oxygen atmosphere of 2 x 10(-6) Torr. The RHEED (reflection high energy electron diffraction) pattern shows diffraction streaks due to the 1 x 1 structure of the Mo(110) surface and diffraction spots from the MoO2 Crystallites. The MoO2 crystallites grow on the Mo surface with epitaxial orientation relationships. The transmission pattern of the MoO2 Crystallites diminished at 1100-degrees-C, indicating that the epitaxially grown crystallites evaporated from the surface. At temperatures exceeding 1100-degrees-C, complex two-dimensionally ordered structures induced by oxygen, appeared. Finally, only the 2 x 2 structure remained. By heating the specimen at 1600-degrees-C in a vacuum of 10(-10) Torr, a Mo clean 1 x 1 structure was obtained.