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A unified theoretical method is established to determine the charge-compensated C3v(Ⅱ)centers of Er3+ions in CdF2 and CaF2 crystals by simulating the electron paramagnetic resonance(EPR)parameters and Stark energy levels.The potential(Er3+-F--O42-)and(Er3+-F1-02-)structures for the C3v(Ⅱ)centers of Er3+ions in CdF2 and CaF2 crystals are checked by diagonalizing 364×364 complete energy matrices in the scheme of superposition model.Our studies indicate that the C3,,(II)centers of Er3+ions in CdF2 and CaF2 may be ascribed to the local(Er3+-F--O42-)structure,where the upper ligand ion F-undergoes an off-center displacement by △Z ≈ 0.3 ? for CdF2 and △Z ≈ 0.29 ? for the CaF2 along the C3 axis.Meanwhile,a local compressed distortion of the(ErFO4)6-cluster is expected to be △R ≈ 0.07 ? for CdF2:Er3+and △R ≈ 0.079 ? for CaF2:Er3+.The considerable g-factor anisotropy for Er3+ions in each of both crystals is explained reasonably by the obtained local parameters.Furthermore,our studies show that a stronger covalent effect exists in the C3v(Ⅱ)center for Er3+in CaF2 or CaF2,which may be due to the stronger electrostatic interaction and closer distance between the central Er3+ion and ligand 02-with the(Er3+-F--O42-)structure.