[en] The first order magnetization process (FOMP) is associated with the irreversible rotation of the magnetization vector Msub(s) between inequivalent states. The critical field Hsub(cr) and the amplitude ΔM of the jump observed in the direction parallel to the applied magnetic field are functions of the anisotropy constants of the crystal. A complete phenomenological analysis is given for the case of uniaxial anisotropy in terms of the first three anisotropy constants K₁, K₂ and K₃, as well as in terms of the anisotropy coefficients chisub(2,0), chisub(4,0), chisub(6,0). Computer plots of the critical parameters and the magnetic phase diagram are given together with an analytical treatment of the problem. The results give a unified view of the FOMP in uniaxial crystals and provide a method for the accurate determination of the anisotropy constants at the temperatures where the phenomenon is present. (orig.)