Group-III-nitride quaternary alloys are useful for blue high brightness light emitting devices and high-temperature,high-power,and high-frequency electronic devices. It is possible to change only the value of the band gap while keeping the lattice parameter at a constant value. The thermodynamical stability of these alloys is obtained analytically using the valence force field(VFF)model for wurtzite structures. The unstable two-phase regions for Al_xGa_yIn_1－x－yN quaternary alloys are calculated,and the formation of In-rich regions are studied with respects to In-In affinity. The calculated results can provide useful guidance in epitaxial growth of AlGaInN on GaN.