The quaternary alloys InGaAsP, matched in their lattice constant to InP, are considered in view of optical-waveguide applications. The parameters, most important in this connexion, are the refractive index n and the optical absorption coefficient α. Both are calculated starting from quantities relevant to the binary constituents of the system InGaAsP. The results are compared with the relatively few experiments reported in the literature. The calculations are applied to film and rectangular waveguides, showing that they are sufficiently low in loss for integrated-optics applications.