The ‘intermediate resonance’ formulation of slowing-down problems is extended to nonhomogeneous systems by means of formulating the integral transport equation for the problem and comparing with the analogous homogeneous system equations. Heavy-atom slowing down in a heterogeneous system is accounted for in this formulation, yet quite concise expressions for resonance integrals are obtained. Numerical results are compared with a Monte Carlo calculation for a specific lattice, and good agreement is obtained. The comparison of homogeneous and nonhomogeneous system equations not only establishes the so-called ‘equivalence relations’ but also clearly brings out the approximations involved in these relations and permits a determination of some of the errors involved. In particular, the ‘flat-flux approximation’ is discussed in detail.