A diffusional model of interface displacement kinetics is proposed for the growth ofnintermediate 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 ofnintermediate phases, unidirectional diffusion flow, and local equilibrium conditions. The velocity of each interface follows the parabolic law and the(n+1)kinetic coefficients are expressed as a function of boundary concentrations and diffusion coefficients of all the phases via(n+1)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 &agr; and &bgr; are such that the chemical diffusion coefficientD&agr;(in &agr;) is smaller thanD&bgr;(in &bgr;), it is found that the interface velocities are enhanced by: (a) increases inD&bgr;,(b) increases in the solubility limit in &bgr;, and (c) reduced miscibility gaps at the interfaces. Moreover, the widths of the intermediate layers are increased by: (a) decreases inD&bgr;and (b) increases in the diffusion coefficients and solubility limits in these intermediate phases. ©1997 American Institute of Physics.