The effect of a mixed crystal transition zone (grading) on the perfection of crystals grown by epitaxial deposition onto substrates of differing lattice parameter and expansion coefficient is considered. The number of misfit dislocations required to compensate lattice mismatch at the growth temperature and magnitude of bending stresses which develop during subsequent cooling have been computed as a function of the width of the transition zone &dgr;. These results have been applied to the case of GaP grown onto GaAs seeds. Using a simple model for lattice displacements, it is predicted that grading does not reduce the number of misfit dislocations but merely distributes them over the width &dgr; so that the density is reduced in proportion to &dgr;−1. The bending stresses in the grown layer are shown to be highly dependent on the width of the transition zone and thickness of the grown layer. Moreover, for a given seed thickness and zone width there is an optimum thickness for the growth layer for which the bending stress is smallest.