CaF2 crystals doped with 0.1 percent GdF3 were observed to develop surface layers when annealed above 700 °C in air, during application of Pt paste electrodes. The conductivity in these surface layers was much higher than in the bulk, due presumably to the large numbers of anion vacancies produced by dissolved oxygen. The presence of these high conductivity surface layers produced a relaxation in the dielectric spectrum with (1) an approximately temperature-independent magnitude, Δκ, (2) a relaxation time controlled by the conductivity of the surface layers, and influenced therefore by heat treatment of the specimen, and (3) an activation energy equal to that for conductivity of the surface layers, about 0.9 eV. This relaxation is sufficiently similar to dielectric relaxations observed previously in ionic crystals and ascribed to defect pairs to suggest that great care must be taken in interpreting dielectric measurements in these materials. What is thought to be dipole relaxation may in fact be due to the presence of thin layers accidentally present on the crystal. There is a marked electrode polarization effect in these crystals. The electrode capacitance at not-too-low frequencies depended upon the frequency and both the number and mobility of the charge carriers with 3/2 power laws.