A method of adaptive nonparametric classification based on counting known points “observed” within a hypersphere inserted in the character space is described. It is shown that an optimal single-hypersphere decision process exists, and that the proposed procedure converges stochastically to the optimal process. The latt)er in turn convrrges at maximum rate to the likelihood ratio decision rule. Sampling experiments on multivariate normal populations indicate that the efficiency of the method when the parametric model holds is about the same as that of the standard parametric procedure.