Stationary transport of a scalar quantity, such as heat, mass of an admixture or electric charge, through a moderately concentrated composite material that contains identical spherical inclusions imbedded into a continuous matrix is considered. The packing of the spheres is locally random but the material is slightly non-uniform in the sense that there exists a gradient of the mean concentration, the linear scale of which is much larger than the size of the sphere. Conduction is shown to be characterized by concentration dependent bulk conductivity coefficients that make up a second-order tensor. In particular, the occurrence of an additional constituent of the transient flux of the quantity which is directed along the concentrational gradient is possible. The conductivities are expressible in terms of two scalar functions of both concentration and its squared gradient which are found for moderately concentrated materials and an arbitrary relation between the conductivities of a pure matrix and of the material of an inclusion.