It is known that in the case of large zero-field splittings (ZFS), which occur between ground state levels of ions with half-integral electron spin S 2 3/2 in a strong axial o r rhombic crystal field, a characteristic angular dependence of resonance magnetic fields for the intradoublet EPR transition -1/2 -+1/2 is observed /1 to 4/. It was also shown /5 to 8/ that, if ZFS is large comparing with the Zeeman splitting, there is an anisotropy of hyperfine splittings of intradoublet transitions for ions with nuclear spin I 2 1/2. In the present paper, the angular dependence of energy levels, resonance fields, and hyperfine splittings of interdoublet EPR transitions for ions with arbitrary values of. S and I in a strong axial crystal field is calculated by perturbation theory.The spin-Hamiltonian for ions with S > 1/2, I 2 0 in the crystal field of axial symmetry is where the various terms have their normal spectroscopic meaning. 8 is the angle between the direction of the external magnetic field and the crystalline axis, which is adopted a s the axis of quantization of the electronic spin. Spin operators of higher order were not included in (I), because in the case of large ZFS their contribution to the energy levels is much l e s s than the axial parameter D and does not lead to an essential change of the angular dependence. In general it is possible to take into account these terms by including them in the value of D, as it was made, for example, in /3/. In the following 1) 378410 Ashtarak 2, USSR.