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A recent formulation of a multiphase-field model is presented. The approach is employed to numerically simulate phase transitions in multiphase systems and to describe the evolution of the microstructure during solidification processes in alloy systems. A new method for modelling solute diffusion in a binary alloy within N different phases with varying solubilities and different diffusion coefficients is integrated in the multiphase-field model. The phase-held/diffusion model derived is compared with the previous Wheeler, Boettinger and McFadden (WBM) model in a limiting case. The set of coupled evolution equations, the phase-field model equations and the concentration field equation is solved using control volume techniques on a uniform mesh. With the input of the specific phase diagram, thermophysical and materials data of the chosen real Fe-C alloy system: the multiphase-field method is successfully applied to compute the peritectic solidification process of steel. The numerical calculations of the peritectic reaction and transformation are presented.