The parameters of the zero-field level splitting of Gd3+ ions localized in three kinds of tetrahedral clusters are estimated within the superposition approximation. The structure of a cluster is determined by minimizing the energy of the crystal with the embedded cluster. As a result, the strong monoclinic EPR spectrum with b 20 = -345 MHz is attributed to the [CdY2CdF26] cluster and a weaker spectrum with b 20 ≈ -600 MHz is attributed to [Cd2YGdF26]. The difference between the absolute values of the calculated and experimental parameters b 20 is explained by the fact that the experimental spectrum is due to gadolinium ions located in clusters that are part of associations. © 2008 Pleiades Publishing, Ltd.