We report on an X-ray diffraction study of the epitaxial growth of thick films of cobalt and nickel disilicides on silicon. The lattice parameters both parallel and normal to the interface are measured at room temperature (RT) for various samples prepared by solid phase epitaxy or reactive deposition epitaxy with annealing at high temperature (600-800 "C). The formation of a rigid disilicide/silicon interface with a dislocation network frozen below a critical temperature TD, estimated at 600 "C for CoSi2 and at 710'C for NiSi2, is the likely growth mechanism of the thick disilicide films. CoSi2 and NiSi2 layers are indeed tetragonally strained at RT with a lateral mismatch equal to that of the relaxed material at TD, i.e. --0.87% and +0.17% respectively. The tetragonal distortion results from the different thermal expansion coefficients of silicon and silicides. Doping NiSi2 with 10% Co, i.e. smaller atoms, leads to a close in-plane lattice match. Introducing 6% Au atoms increases the lattice parameter of NiSi2, and also favours the relaxation of the film after annealing. With 12% Au-doping, quasi-total relaxation is observed but the layer is no longer uniform. Doping in all cases induces a decrease of the critical temperature To of dislocation freezing.