The behavior of uniaxial paramagnets in a tilted magnetic field is considered as a function of temperature. The structure of the energy spectrum as well as magnetization and susceptibility components are determined. Exact formulas for the spinS=1/2are obtained. Thermodynamic parameters of the system are studied for arbitrary values ofSin an easy-axis and easy-plane cases in different approximations (weak and strong magnetic fields, low and ultralow temperatures, etc.). It is shown that in the easy-plane case, the transverse magnetization and longitudinal susceptibility as functions of magnetic field at low temperatures exhibit peculiarities in the form of a series of sharp spikes, while the longitudinal components of these quantities in the easy-axis case display only a single spike. ©1998 American Institute of Physics.