A generalization of the model of Burton, Cabrera and Frank of step flow epitaxial growth on vicinal surfaces in multi-component systems is presented. In particular, the present model addresses chemical vapour epitaxial growth, where the atomic or molecular species composing the crystal, or growth units, are carried to the substrate inside more complex molecules, or precursors, as well as molecular beam epitaxial growth of compound semiconductors. Surface diffusion, chemical reactions, and incorporation at steps are included in the model, that allows for an analytic computation of the growth rate. Special attention is paid to the delicate problem of boundary conditions at steps in a two-component system. (C) 2003 Elsevier B.V. All rights reserved.