(Zn,Cd)Te/CdTe strained layer superlattices have been grown by molecular-beam epitaxy on CdTe(100), InSb(100), and GaAs(100) substrates and substrate/buffer layer combinations. Superlattice period thicknesses ranged from 90 to 330 Å; total superlattice thickness was 0.8 or 1.6 μm. The ratio in thickness between the (Zn,Cd)Te and CdTe layers was tailored to allow the in-plane lattice parameter of a freestanding superlattice to match that of Hg0.8Cd0.2Te. A high degree of structural quality is indicated by the existence of multiple satellite peaks in the x-ray diffraction spectra from these structures. Structural quality is found to depend on the substrate used.