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A diffusional model of interface displacement kinetics is proposed for the growth of n intermediate compounds at an initially planar interface between two semi-infinite phases. The model is based on the solution of Fick's equations with the restrictive assumptions of simultaneous growth of n intermediate phases, unidirectional diffusion flow, and local equilibrium conditions. The velocity of each interface follows the parabolic law and the (nϩ1) kinetic coefficients are expressed as a function of boundary concentrations and diffusion coefficients of all the phases via (nϩ1) nonlinear equations. A parametric study of the kinetic coefficients, corresponding to realistic situations of initial solid-solid or solid-liquid interface, is developed for systems with one or two intermediate layers. If two interacting initial phases ␣ and ␤ are such that the chemical diffusion coefficient D ␣ ͑in ␣͒ is smaller than D ␤ ͑in ␤͒, it is found that the interface velocities are enhanced by: ͑a͒ increases in D ␤ , ͑b͒ increases in the solubility limit in ␤, and ͑c͒ reduced miscibility gaps at the interfaces. Moreover, the widths of the intermediate layers are increased by: ͑a͒ decreases in D ␤ and ͑b͒ increases in the diffusion coefficients and solubility limits in these intermediate phases.