In solid solutions of alkaline- and rare-earth fluorides with a fluorite structure, ions of most elements of the rare-earth (RE) row form hexameric clusters that assimilate the minor component of the solid solutions (fluorine) and build it into the cubic fluorite lattice without changing its shape. An analysis of the EPR spectra of paramagnetic RE ions (Er3+, Tm 3+, Yb3+) in clusters of diamagnetic ions (Lu 3+, Y3+) confirms their hexagonal structure, which was established when studying the superstructures of the compounds under study. In such a cluster, a RE ion is in a nearly tetragonal crystal field, with the parameters of this field differing radically from those of single cubic and tetragonal RE centers in crystals with a fluorite structure. In particular, this field causes high (close to limiting) values of the g∥ factors of the ground states of the paramagnetic RE ions. Computer simulation is used to determine the atomic structure of a hexameric cluster in MF2 crystals (M = Ca, Sr, Ba). The crystal field and energy spectrum of Er 3+, Tm3+, and Yb3+ ions in such clusters are calculated, and the spectroscopic parameters of the ground states of these ions are determined. The calculations confirm the earlier assumption that the unusual EPR spectra of nonstoichiometric fluorite phases are related to RE ions in hexameric clusters. © 2005 Pleiades Publishing, Inc.