Powder and double-crystal x-ray diffraction were used to study the structural properties of highly strained (GaAs)«/(GaP)M short-period superlattices grown on GaAs (001) substrates. In spite of the large lattice mismatch (f = 3.6%) between GaAs and GaP and the competition for incorporation between As and F» high-quality short-period superlattices of GaAs/GaP have been grown by a development of conventional molecular beam epitaxy named atomic layer molecular beam epitaxy. The in-plane lattice parameter (ay) of the different superlattices was measured and studied as a function of the GaP content. We found that, for a given total superlattice thickness of 4000 A, the critical lattice mismatch is fc ~ 0.5% (corresponding to an average GaP content of 13.6% in the superlattice). This means that for an average misfit or lattice mismatch above fc the superlattice starts to relax. This experimental result is compared with predictions of critical thickness theories based on energy criteria. A clear relation of the degree of relaxation with peak width of the superlattice zeroth-order diffraction peak is found. High-resolution transmission electron microscopy has been performed to analyse the type of dislocations that relax the mismatched layers. © 1993 IOP Publishing Ltd.