The importance of atomic relaxations, chemical disorder, and epitaxial constraints on the band gap of random, anion-mixed nitride alloys GaPN and GaAsN have been investigated, via pseudopotentials calculation. It has been demonstrated that simple approximations such as the virtual crystal approximation, or the use of high-symmetry ordered structure to mimic a random alloy, or the neglect of atomic displacements, are inadequate. It is found that a fully relaxed, large supercell calculation reproduces well the experimental band gaps of GaPN and GaAsN films. ©1997 American Institute of Physics.