The formation of metastable, inhomogeneous solid solutions during the crystallization of mixed systems is a well-known and often inconvenient phenomenon, which limits the reliability of calculations based on equilibrium. In this paper we present a relatively simple kinetic model that describes the evolution of a crystallization process in a finite, multicomponent system, represented by crystallization curves. The kinetic model is applied to fat mixtures, used as model systems, with up to 10 components, and the resulting metastable states are compared with the equilibrium predictions. The deviations from equilibrium strongly depend on the thermodynamic properties of the individual, pure components, the mixing properties, the presence of a solvent, and the undercooling. Generally it holds that the solid phase fraction predicted by the kinetic model is lower than that of the equilibrium state.