SUMMARY A general equation for determining the effective thermal conductivity, Kij, of composite materials is developed in terms of volume averages of the local properties. The special case of infinitely dilute dispersions is considered in detail. It is shown that, here, Kij is a symmetric tensor which, using the methods of potential theory, is obtained explicitly as an infinite series in (1−α)/(1+α), convergent for all α, where α is the ratio of the conductivities of the dispersed phase to that of the continuous phase. The coefficients in this expansion are shown to depend exclusively on the geometry of the dispersed phase and to involve only integrals over the surface of the inclusion. From this general expression it becomes evident that, to first order in α−1, Kij is isotropic and that it has the same value for a given volume concentration, ϕ, of the dispersed phase irrespective of the shape of the latter.