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 (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 α and β are such that the chemical diffusion coefficient Dα (in α) is smaller than Dβ (in β), it is found that the interface velocities are enhanced by: (a) increases in Dβ, (b) increases in the solubility limit in β, and (c) reduced miscibility gaps at the interfaces. Moreover, the widths of the intermediate layers are increased by: (a) decreases in Dβ and (b) increases in the diffusion coefficients and solubility limits in these intermediate phases. © 1997 American Institute of Physics.