A general solution for the diffusion equation applied to moving interfaces in multicomponent systems is presented. The solution is simultaneously solved with the chemical potential equations describing multicomponent thermodynamic equilibrium, ensuring local equilibrium at the interface. Phase kinetics and thermodynamics are rigorously linked irrespective of the number of solutes in the system and their difference in diffusivity. The mathematical compactness of the equations resulted in an increase of the computations speed as compared to other approaches. The model is applied to calculate the reaustenitisation kinetics for TRIP and Dual Phase steels with four and more components. The progress in ferrite, cementite and austenite compositions and volume fraction for a variety of heating rates and isothermal holding temperatures is presented.