During the long-term corrosion of nuclear waste glasses under nuclear waste disposal conditions, the precipitation of zeolitic phases has been linked to a delayed acceleration in glass corrosion (known as “Stage III”). Hence, predicting the thermodynamic propensity for zeolites to form upon the dissolution of nuclear waste glasses is key to ensure their long-term performance. Here, we compile a unified, internally-consistent thermodynamic database “clay20” to estimate the stability of clay and feldspar phases relevant to nuclear waste immobilization glasses, including beidellite(Mg, Ca, Na, K), kaolinite, montmorillonite(Mg, Ca, Na, K), nontronite(Mg, Ca, Na, K), saponite(Ca, Na, K), and albite. Based on this, we report a geochemical modeling method allowing us to predict the stability of secondary phases (including zeolites, calcium–silicate–hydrate gels, and clays) upon the dissolution of nuclear waste immobilization glasses. We show that this approach offers a realistic description of the stability of the secondary phases forming during the dissolution of two archetypical model nuclear glasses (namely, the International Simple Glass, ISG, and WVUTh-203) under conditions relevant to nuclear waste disposal (T = 90 °C, p = 1 bar) as a function of pH. We find that the formation of silica and clay secondary phases is thermodynamically favored at low pH (pH < 10), whereas, in contrast, zeolite (analcime) and calcium–silicate–hydrate phases are favored at high pH (pH > 10.5). This suggests that thermodynamics (i.e., not solely kinetics) might play a key role in determining the range of solution pH wherein stage III corrosion may occur, i.e., when zeolite formation is favored.