A non-parametric stereological method for the estimation of distributions of distances (d) between paired spheres of the same size, from the distances between their profiles observed in sections, is presented. The model accounts for sphere overprojection and truncation effects. Using the mean value of d (d), it is then possible, with simple formulae, to compute the probabilities of the co-observation of two profiles from paired spheres with distance d between their centres, when at least one profile is observed. A useful application is the estimation of true binucleated cell frequencies from observations on tissue sections. An example for rat liver diploid cells is shown. The sphere distribution must be studied beforehand and, when the size variation is unacceptably large, implying that the assumption of a constant sphere radius is unreasonable, the main limitation of the model is met.