Abstract. The superionic conductivity and dielectric response of heavily doped fluorite-structured Ba~_xRxF2+x (R = La, Pr, Nd, Gd, Tb, Y, Sc; x = 0.005 -0.45) crystals are reported. The highest ionic conductivity is found for R = Sc and x = 0.1. Upon ScF 3 doping, small Sc 3+ ions rearrange their surroundings, create excessive fluoride interstitial ions and bring about a high ionic conductivity. For each dopant, the concentration dependence of the ionic conductivity is non-linear. A monotonous concentration dependence of the ionic conductivity is found only for La 3+ doping. Upon doping with Nd 3+, Gd 3+, Tb 3+, y3+ and Sc 3+ ions, a conductivity maximum is observed at x = 0.1 -0.2. Upon Pr 3+ doping, this maximum is split. The influence of defect clustering on the concentration dependence of the conductivity is discussed.