Several density functional theory based methods and the ab initio MP2 method were used to investigate the mechanism of secondary-secondary, tertiary-tertiary, and secondary-tertiary hydride-transfer reactions between alkanes and alkylcarbenium ions. All these reactions were found to proceed through a mechanism consisting of two steps : formation of a stable tight intermediate complex and decomposition of the complex to the products without activation energy. The optimized geometry of all the intermediate complexes is linear, with an open three-center two-electron C-H-C bond that is more or less symmetrical depending on the nature of the involved carbon atoms. Hy comparison of the results obtained at different levels of theory, it was shown that DFT-based methods provide optimized geometries in very good agreement with those obtained at the MP2 level, but the former fail in describing the energetics of the complex formation reactions studied. While DFT underestimates in some cases the stability of the intermediate complexes, the MP2 results are in very good agreement with the experimental data, indicating the adequacy of this method for studying this type of reaction mechanism. It was also shown that when large systems are involved and geometry optimization and characterization of the stationary points at the MP2 level become computationally too expensive, MP2 single-point calculations on DFT-optimized geometries yield results of comparable quality. Finally, energy profiles along the reaction coordinate were calculated for the three types of hydride-transfer processes considered, and neither a loose complex nor an internal potential barrier was found for any of them.