Grazing-incidence x-ray diffraction, a surface-sensitive technique, has been used to obtain structural details parallel to the interface of an epitaxial system, such as lattice parameters, strain, crystallite size and orientation, on films with thicknesses ranging down to a few mono-atomic layers. Tungsten grows epitaxially on the (1102) plane of sapphire, with the orientation W (001) ∥ Al2O3 (1102) and W  ∥ Al2O, . Sufficient diffraction intensity for characterization could be obtained from ∼30A-thick W films. Layers of GaAs can be grown epitaxially on the basal plane of sapphire with the orientation GaAs(111) ∥ Al2O3(00.1) and GaAs  ∥ Al2O3. Niobium films grow on GaAs (001) and (111) substrates with a (001) plane parallel to the interface, whereas molybdenum films prefer to grow with a (111) plane on both substrates. The best orientation, i. e. the smallest mosaic spread, of the film is obtained when the substrate plane has the same symmetry as the preferred film growth plane. In all these cases with relatively large misfit, the strain observed parallel to the interface is only a small fraction of the theoretical misfit strain, indicating the relief of the misfit strain within the first few atomic layers.