A comprehensive study of the manifestation of proton transfer in the mono- and the dihydrated complexes of hydrogen fluoride and hydrogen chloride is presented. This includes a general ab initio study at the Hartree-Fock and at the second-order Moller-Plesset (MP2) levels of approximation, in vacuo and in simulated polar and nonpolar solvents, by means of the self-consistent reaction field approach, using the extended split-valence type 6-31+G** basis set. The potential energy surface along the hydrogen-bond coordinate, for the two monohydrated complexes, in a gas-phase or in a nonpolar solution, is generally flat, displaying a single minimum, which corresponds to a hydrogen-bonded molecular complex. Unlike the weak acid/weak base H2O...HF complex, a second minimum is observed at the Hartree-Fock level when the strong acid/weak base H2O-HCl complex is embedded in a highly polar environment. However, the inclusion of intramolecular electron correlation causes this minimum to vanish, therefore indicating that (i) the acidity of hydrogen chloride is not strong enough to yield proton transfer, (ii) the mechanism accounting for the protolytic dissociation should involve more than a single water molecule, and (iii) the stabilization of the H3O+...Cl- complex, characterized by the emergence of a second minimum, is likely to be related to the general trend of the Hartree-Fock approximation to neglect dispersion. The incorporation of a second water molecule, as an attempt to increase by cooperative effect the donor character of the oxygen atom directly bound to the hydrogen halide, leads to a similar artifact when (H2O)(2)...HCl is surrounded by a nonpolar solvent. In contrast, the presence of an energy minimum corresponding to an (H2OH+...Cl- ionic complex, at both the Hartree-Fock and the MP2 levels of approximation, in a moderately polar solution, supports the view that (i) two water molecules are required in this kind of acidic dissociation and (ii) there is no explicit participation of the hydronium ion (H3O+) in the course of the process. Finally, whether the solvent is polar or not, there is no evidence of proton transfer in the dihydrated (H2O)(2)...HF complex, hence suggesting that the protolytic dissociation of hydrogen fluoride might imply additional water molecules.