A theory of two-phase eutectic growth for a multicomponent alloy is presented. Using the same hypotheses as the Jackson-Hunt theory, we find that the growth law of the microstructure given by Jackson and Hunt for binary alloys can be generalized to systems with N elements. Thermodynamic parameters involved in this theory are linked to the Gibbs free energies of the phases which makes it possible to compute these parameters with CALPHAD tools. A model is derived from this general theory for ternary alloys which does not contain any assumptions on the alloy thermodynamic properties, contrary to previous models. We find that a small addition of a ternary alloying element with a small diffusivity to a binary alloy can significantly alter the spacing of the eutectic.