GaInAsP quaternary alloys for the wavelengths near 1.3 and 1.55 μm have been grown on InP(001) substrates by gas-source molecular beam epitaxy. Unstable growth related to (miscibility gap induced) composition modulations was found to occur in these alloy compositions. The dependence of stability of the growth on the growth conditions has been studied. Strain, substrate temperature and growth rate were found to have an important effect on the material quality. The layers grown in unstable regions of the growth parameter space exhibited degraded quality according to X-ray diffraction, photoluminescence, Hall measurements, transmission electron microscopy and inspection of the surface morphology. However, the growth conditions for good-quality material could also be found.