Abstract. The paper is devoted to the study of the effective conductivity k^* of a random dilute dispersion of spheres. A special attention is paid to the c²-coefficient a₂ in the expansion of k^* in powers of the volume fraction c of the spheres. The functional dependence of a₂ upon the radial distribution function is discussed and it is shown, using simple arguments, that a₂ is a sum of a constant and a linear functional of the said function. The analytical form and certain estimates for the kernel of this functional are obtained in the two-dimensional case (fiber-reinforced material).