For two-sublattice magnetic systems with single-ion and exchange anisotropy and arbitrary spin, the parametric Green's functions describing the thermodynamic behavior of the systems in the eollinear phases are calculated. An analysis of the obtained solutions shows that of the $4S$ energy branches that characterize the excitation spectrum of the magnets just two collective modes are dominant at low temperatures. It is also noted that the appearance in the region of orientation phase transitions of aetivationless modes in the energy spectrum of uniaxial systems leads to low-temperature divergences of the susceptibility of the paraprocess. The number of divergences must be equal to the number of critical fields.