Gamma ray spectroscopy has become, during the past several years, a widely used technique for the assaying of a mixture of gamma-emitting radionuclides with minimum sample alteration. As a result, considerable savings in time and labor have been achieved due to the reduction of the number of samples requiring extensive radiochemical analysis. The purpose of this paper is to present an optimal method of estimating the amount of each radionuclide present in a mixture when certain conditions are satisfied.