The relaxation process in InGaAs/GaAs heterostructures with a small lattice mismatch (less than 1%), grown by metalorganic vapour-phase epitaxy (MOVPE), has been investigated by means of high-resolution X-ray diffraction (HR-XRD). Transmission electron microscopy (TEM) revealed a two-dimensional (2D) network of 60 degrees misfit dislocations formed at the (0 0 1) interface in the two orthogonal < 110 > crystallographic directions. The structural analysis by X-ray diffractometry was performed with the samples oriented either in the [ 110] or the [110] perpendicular directions, using reciprocal lattice mapping. The observed anisotropic-strain relaxation, related to the asymmetry in the formation of a and beta misfit dislocations along [110] and [110] directions, respectively, causes distortion of the epilayer unit cell and lowers its symmetry to orthorhombic. (c) 2008 Elsevier B.V. All rights reserved.