An analysis of radiant interchange is made which takes account of possible surface variations in incident radiation flux, heat transfer, and leaving radiant flux. This represents a generalization of standard calculation methods which postulate that the radiant fluxes and heat transfer are uniformly distributed on a surface. Consideration is given to pairs of simply‐arranged surfaces having different emissivities, one of which is essentially black. The surface temperatures may be arbitrarily different. The generalized analysis reveals that there may be significant variations in the local heat transfer along a surface, and this stands in contrast to the results of standard (and more approximate) calculation methods. The over‐all heat transfer results are also compared with those predicted by the standard calculation procedure. For the surface which is essentially black the errors arising in the standard procedure are found to be tolerable as long as the net over‐all heat transfer exceeds 20% of the radiant emission. For the nonblack surface the two methods are in agreement.