Lattice-matched ZnSe/InxGa1-xAs heterostructures were fabricated by molecular beam epitaxy on GaAs(001)2x4 surfaces. We find that the partial character of the strain relaxation within the ternary layer can be compensated by a suitable excess in the In concentration to match the free-surface lattice parameter to ZnSe. The surface of the II-VI epilayer, however, exhibits a cross-hatched pattern of surface corrugations oriented along orthogonal  directions. This complex surface morphology reflects the formation of surface slip steps during the nucleation of dislocation half-loops at the surface and the establishment of the misfit dislocation network at the InxGa1-xAs/GaAs interface. (C) 1998 American Institute of Physics.