A model of magnetic and magnetoelastic properties of intermetallic compounds has been considered with the inclusion of the influence of the “giant” magnetoelastic coupling and the biquadratic exchange interaction. The phase transitions as a function of material constants and temperature have been investigated in the framework of the proposed model. It has been demonstrated that the ferromagnetic and quadrupole phases can be formed in the system under consideration. In this case, the phase transition between these phases is a first-order transition and occurs through the intermediate, i.e., quadrupole-ferromagnetic, state. The dependences of the phase transition temperature on the Heisenberg and biquadratic exchange interaction constants have been obtained for compounds of the terfenol-D type.