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Magnesium alloys are becoming increasingly important for weight reduction of components in transportation and electronic industry. The solidification microstructure of most Mg-cast-alloys is dominated by the hexagonal closed-packed structure of the Mg solid solution. Nucleation and dendritic growth of this phase strongly depend on the alloy composition, the process parameters and on the size and number of nucleant particles. The general aim of the present work is to examine these dependencies in order to assist the design of improved alloys and processes. Therefore, a multiphase-field model for multicomponent alloys is adapted to magnesium-based alloys. A hexagonal anisotropy function is integrated to describe the growth of the hcp-magnesium phase and a special nucleation model addresses heterogeneous nucleation on grain refiner particles. Simulations are run by online-coupling of the phase-field software to a thermodynamic calculation software using a Calphad database for the Mg-Al-Zn-Mn system. Applications to the commercial Mg-Al-Zn based alloy AZ31 are presented, showing directional as well as equiaxed dendritic growth.