The catalytic action of H+ and BF3 in the reaction between CH4 and HF, taken as a model of a Friedel-Crafts reaction, has been theoretically studied by means of ab initio methods using the split-valence 3-21G basis set. It has been shown that the formation of a complex with the catalyst increases the electrophilic character of hydrogen fluoride. As a direct consequence the potential energy barrier of the electrophilic attack step is drastically diminished, especially in the case of catalysis by H+. When the reaction is catalyzed by BF3, two different mechanisms have been investigated. While one of them corresponds to a traditional acid catalysis, in the other one BF3 acts as a bifunctional catalyst, this latter being clearly more efficient. The reasons which permit us to understand these different kinds of catalytic action have been carefully analyzed. © 1988.