We report the epitaxial growth of single phase (001)-oriented thin films of Fe2+xTi1-x in the C14 Laves phase stability range using molecular beam epitaxy (MBE). The growth was studied by reflection high-energy electron diffraction (RHEED) and X-ray diffraction (XRD). The onset temperature for epitaxial growth and the temperature range for improved crystalline coherence were identified. From X-ray reflectometry analysis the rms roughness was estimated to 0.5 nm for typical film thicknesses of 22 nm. As revealed by scanning tunneling microscopy (STM), this roughness is discrete and due to step edges corresponding to the full c-axis length of Fe2Ti. The epitaxial growth implies an extended range of homogeneity as compared to bulk samples, A strong dependence of the growth behavior on the composition within the range of homogeneity was observed exhibiting increased crystalline coherence at higher iron concentrations. Furthermore, the volume increase of the unit cell with the Ti concentration is compatible to Vegard's law. Evidence for an iron-induced surface reconstruction was found in RHEED investigations. (C) 2002 Elsevier Science B.V. All rights reserved.