The results of a detailed optical and paramagnetic-resonance study performed on copper in CaF2 and silver in BaF2 are presented. Two different Ag+ centers were identified in BaF2. One is associated with an interstitial F- ion whereas the other one has a cubic surrounding. The Cu2+ ion in CaF2 was shown to reorient at 4.2 K between 6 equivalent minima of D2h symetry. This fact is interpreted with the aid of a T2gx(T2g+Eg) type Jahn-Teller effect. The nonlinear mixed coupling terms are shown to play an important role. The Cu+ impurity in CaF2 is presumably off-center in the F- sublattice without associated defect or impurity.