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The growth of the delta-ferrite and gamma-austenite from the liquid, the peritectic reaction and the peritectic transformation are studied using a new multi phase field model. This approach describes the evolution of the three possible interfaces (liquid-ferite, liquid-austenite, ferite-austenite) as well as the triple point situation (liquid-ferite-austenite). The phase field equations are coupled to the diffusion equation of carbon. The local equilibrium concentrations at the interfaces are taken from the metastable phase diagrams calculated using a commercial thermodynamic database. The deviation from the local equilibrium concentration determines the local undercooling of the system and represents accordingly the driving force for the phase transitions. As a first simulation step the model has been applied to a low carbon FeC for a simple solidification scenario. A system is cooled with a constant cooling rate. When the temperature falls below the peritectic temperature, the austenitic phase is nucleated ahead of the primary ferrite phase. The mean fraction solid of the system, representing a fundamental microstructure parameter for non-equilibrium processes is determined by averaging the local phase fractions within the calculation area.