The initial dissolution rate of a series of multicomponent glasses is studied in order to discuss the influence of increasing magnesium content in the glass on this alteration regime and to highlight differences in behavior between calcium- and magnesium-bearing glasses. The application of MD-based topological constraint theory (TCT) is confronted to glass transition temperature ( T g ) and initial dissolution rate ( r 0 ) on a glass series containing the main oxides of a French nuclear glass (AVM). In addition, a comparison between a reference magnesium-containing nuclear waste glass, AVMV4 and a proposed derived simplified composition N19M8 is performed regarding r 0 values. Results indicate a similar behavior in this alteration regime for the two glasses, suggesting that this simple glass might be a good analogue to the complex one. Substituting calcium for magnesium decreases the initial dissolution rate by a factor two in the series, while an overall increase of magnesium leads to an increased dissolution rate. Analyses performed with TCT suggests that magnesium environment is better defined than calcium or sodium and may behave as an intermediate species. Finally, a correlation between the number of constraints per atom and T g is established, while the model failed to link structural features to r 0 .