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Crystallization is a major challenge in metallic glass production, and predictive models may aid the development of controlled microstructures. This work describes a modeling strategy of nucleation, growth and the dissolution of crystals in a multicomponent glass-forming system. The numerical model is based on classical nucleation theory in combination with a multicomponent diffusion-controlled growth model that is valid for high supersaturation. The required thermodynamic properties are obtained by coupling the model to a CALPHAD database using the Al-Cu-Zr system as a demonstrator. The crystallization of intermetallic <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mfenced separators="" open="(" close=")"><mi>Al</mi><mo>,</mo><mi>Cu</mi></mfenced><mi>m</mi></msub><msub><mi>Zr</mi><mi>n</mi></msub></mrow></semantics></math></inline-formula> phases from the undercooled liquid phase were simulated under isothermal as well as rapid heating and cooling conditions (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mn>10</mn><mrow><mo>−</mo><mn>1</mn></mrow></msup><mrow><mo>–</mo></mrow><msup><mn>10</mn><mn>6</mn></msup><mspace width="4pt"></mspace><msup><mi>Ks</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula>). The obtained time–temperature transformation and continuous-heating/cooling transformation diagrams agree satisfactorily with the experimental data over a wide temperature range, thereby, demonstrating the predictability of the modeling approach. A comparison of the simulation results and experimental data is discussed.