Analytic solutions have been found for a system of nonlinear integro‐differential equations describing compositional changes and sputtering of materials under ion bombardment in planar geometry. These solutions refer to the stationary (high‐fluence) limit and were found by adopting feasible expressions for intermediate quantities from which both input and output can be derived. Explicit examples include sputtering, collisional mixing, and relaxation, but the method allows inclusion of a wider variety of effects. ©1995 American Institute of Physics.Multicomponent materials like alloys, compounds, and isotopic mixtures undergo composition changes under ion bombardment as a result of preferential sputtering and Gibbsian segregation at the surface, ion implantation and mixing in the region penetrated by the incident beam, and defect‐assisted processes that may affect a wider region. A theoretical scheme describing compositional changes in planar geometry was presented many years ago. Its ingredients were (i) a relocation operator accounting for atomic mixing and preferential sputtering, and (ii) a relaxation term ensuring stability of the target as well as adjustment of the depth scale such that the target surface is located at depthx=0 at any time. The scheme has been expanded recently such as to allow inclusion of all athermal and thermal processes leading to compositional changes. The essence is a set of nonlinear integro‐differential equations of the form