A thermodynamic analysis of surface-phase equilibria in the MBE growth of In_1-xGa_xAs layers on lattice-mismatched GaAs and InP substrates is done. It is shown that, in In-stabilized conditions, the substrate-induced strain enhances the arsenic equilibrium pressure over In-Ga-As liquid phase in the whole range of the solid phase composition in the case of GaAs substrate, whereas in the case of the InP substrate, the pressure is enhanced by the strain at x<0.47 and lowered at x>0.47. For both substrates, locking the surface monolayer composition occurs. In the As-stabilized conditions, the strain results in the lattice-pulling effect. [DOI: 10.1380/ejssnt.2006.53]