The incorporation of the group V components in In1−xGaxAsyP1−y, grown lattice matched to InP by gas source molecular beam epitaxy, has been studied over the entire alloy range, 0≤y≤1, as a function of the group V source composition, the V/III beam flux ratio, and the substrate surface orientation. Several aspects of the group V incorporation are most easily understood in terms of a simple model involving a constant incorporation coefficient and an As ‘‘underpressure’’ condition. An improved description of the results at lower values of the V/III flux ratio is provided by a thermodynamic model based on equilibrium reactions for the formation of the binary constituents, and using the bulk properties of the solid solution. However, the thermodynamic model is quantitatively incorrect for large values of the V/III flux ratio. Furthermore, the results for different surface orientations reveal additional weaknesses in the thermodynamic model and suggest the need to account for the surface bonding configurations in describing the group V incorporation in epitaxial growth. ©1996 American Institute of Physics.