Precise x-ray diffraction measurements between room temperature and ∼400 °C (Bond method) exhibit some details in the variations of strain in ∼ 1 μm thick epitaxial layers of GaAs, InP, CdTe, EuS, or SrS on Si or GaAs substrates. The lattice parameters of the cubic layers, which are deposited at high temperatures, deviate from the lattice parameters, a0, of small unconstrained single crystals by Δa/a0 = ∈0 ≲ 10−3. The layers adhere to the substrates below Tc and adopt different strains, ∈‖ and ∈⊥, parallel and perpendicular to the substrate. Frequently the Tc and ∈0 values vary on annealing at 160–400 °C. The ratio E = —(∈⊥ — ∈0)/(∈‖ — ∈0) remains constant for each sample. The change of the relative volume ΔV/V0 = ∈‖ (2—E) +∈0 (1 + E) at the variation of ∈0 can give rise to corrugations, blisters, or microcracks in the epitaxial layers. Stable epitaxial layers with constant ∈0 and Tc values can be obtained by deposition on buffer layers or stepped substrates.