Epitaxial double layers of CdS and CdTe have been grown on GaAs by close-spaced chemical vapor transport, to study the growth of CdTe on various CdS surfaces. Since the [00.1] axis of CdS aligns to one of the 〈111〉A axes of the GaAs substrate, the deposition of CdS on {111̄}A, {110}, and {100} GaAs surfaces yields approximately the {00.1}, {10.3}, and {11̄.1} CdS surfaces. On {111̄}A and slightly inclined substrates the CdS-CdTe layers (2-10 μm thick) grow uniformly thick with smooth surfaces. On the {110} and {100} faces the CdTe layers show a scale structure through the whole layer, which is approximately aligned to one of the 〈111〉 axes of the substrate. X-ray investigations reveal three- and two-dimensional lattice defects in the CdTe layer such as twinning, cubic-hexagonal mixture, stacking faults, fiber texture, and polycrystallinity. The number of defects increases in layers grown on {111̄}A to {110} and to {100}. The most perfect layers on {111}A faces and slightly inclined ones have a cubic structure with twinning about the growth direction. On {110} and {100} faces, the [00.1] and [111̄] stacking axes of the three lattices are slightly tilted to each other. The tilt angle can be explained by an accommodation of the lattice mismatch at the interface in such a way that the stacking planes join together continuously at the boundaries.