This paper proposes a contribution to understanding the alteration of high-level waste glasses. Numerical simulations, based on a Monte Carlo model, have been performed in parallel to static dissolution tests on simplified glasses. The leaching of borosilicate glasses has been investigated for various compositions containing three or four oxides, which have been derived from the French nuclear glass composition. The comparison between experimental data and simulations allows a precise understanding of the role of each element. The degree of alteration is shown to result from a competition between the irreversible extraction of the soluble species (boron and alkalis) and the reversible dissolution-condensation dynamics of silica, which make possible the restructuring of the surface layer into a passivating layer. The model explains how the surface layer is responsible for the blocking or, at least, for a considerable slowing down of the alteration. It is also able to explain a quite unexpected result, namely, the fact that the replacement of silica by more insoluble oxides (zirconium or aluminum oxides) actually induces an increase of the degree of alteration. This is due to the slowing down of the surface layer reconstruction that delays the alteration blocking.