This paper provides nonparametric empirical Bayes (EB) solutions to two-tail test   in the exponential family  , under the standard product loss function which is proportional to (θ-θ1) (θ-θ2) for incorrectly accepting H₁. Based on empirical data X₁,…X_n, and the present data X from   nonparametric (in the sense that G is completely unknown and unspecified) EB test procedures are proposed. These procedures are asymptotically optimal (a.o.) whenever   Further, for every integer s > 0 a class of non-parametric EB test procedures is proposed. These procedures are shown to be a.o. with rates   for 0 < λ ≤ 2 satisfying certain conditions. Examples of exponential families and gamma densities are given where these conditions reduce to some simple moment conditions on G. No assumption on the smoothness of the function u(.), (and hence of the density function of X), is made at all for any of the results of this paper. By an example of a family of distributions, it is demonstrated that the rates arbitrarily close to o(n_-1) can be attained by these procedures in some situations. It is noted, however, that the actual rates of convergence really depends on the nature of the unknown prior distribution G.