[en] During their aqueous alteration, AVM French nuclear glasses exhibit a large range of behaviour, in spite of a small range of composition. AVM glasses alteration rates are controlled by two phenomena: (i) precipitation of secondary phases, mostly aluminous hectorites, and (ii) diffusion of water across a more or less protective gel. The magnesium contained in these glasses increases the precipitation of these secondary phases, leading to a partial or total dissolution of the gel layer. This dissolution increases the glass alteration rates. On the other hand, Mg also incorporates in the gel, increasing his passivation properties. The predominance of one of these two phenomena depends on the initial composition of the glass, the pH of the solution, and the alteration conditions. In presence of Bure geological disposal site water (Mg and Ca rich), AVM glasses undergo less alteration than in initially pure water, in spite of larger amounts of secondary phase precipitates. This results from incorporation of calcium in the gel instead of sodium and magnesium, improving its passivating properties. We have adapted the geochemical GRAAL model for AVM glasses. In spite of its limitations, this model allows us to describe the differences of behaviour between these glasses, in function of their composition. Moreover, GRAAL can be proposed as a basis of a future operational model for predicting the alteration of AVM glasses. (author)