Nuclear spin relaxation (NSR) and electrical conductivity measurements were performed between about 1 K and room temperature in various fluoride glasses. The19F NSR rates are found to exhibit a pronounced peak around 10 K which is not observed by conductivity experiments. The underlying relaxation process is interpreted by magnetic fluctuations between neighbouring19F nuclear probes without accompanying charge motions. The observed NSR rates and conductivities can be described phenomenologically in the context of excitations of asymmetric double well potential (ADWP) configurations intrinsic to the glassy state.