Quantum reactive scattering calculations for the X + F 2 → XF + F (X = Mu, H and D) and F + XF → FX + F (X = Mu and H) reactions were performed on a global potential energy surface developed at an ab initio multi-reference configuration interaction level. Rate constants for the former reaction were estimated with the J-shifting approximation and compared to previous experimental measurements. A strongly curved behavior observed in the experimental Arrhenius plot was reproduced by the present quantum calculation at a fairly good level. The calculated reaction probabilities for the Mu-exchange reaction show sharp resonance structures around the asymptotic levels. It has been found that the observed resonances are mainly associated with the F⋯MuF complex. Due to the strong coupling between resonance effects and tunneling effects in this heavy–light–heavy system, it is found that the reaction probability is significantly enhanced around the threshold energy.