The EPR spectra of Gd3+ tetragonal centers in crystals with a scheelite structure are analyzed. It is found that the EPR spectra exhibit additional signals in the vicinity of coincidence of the resonance lines attributed to Gd3+ EPR transitions. It is shown that these signals are caused by averaging (due to relaxation spin-lattice transitions between the resonance doublets) of the internal part of the quasi-symmetric system of spin packets corresponding to the inhomogeneously broadened initial EPR lines. The quasi-symmetric arrangement of the spin packets is associated with the mosaic structure of the studied crystals.