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We present an approximation for the treatment of two interacting magnetic impurities immersed into a noninteracting metallic host. We qualify the approximation by investigating the uncoupled case and conclude that the two-impurity approximation is equally accurate as its single-impurity counterpart. The physical properties of the two-impurity Anderson model are first investigated in some limiting cases. In a regime where each of the uncoupled two impurities would exhibit a pronounced Kondo effect, we ignore the indirect coupling via the conduction band and only incorporate direct interactions. For the general case of only indirect coupling via the conduction band, the results show signatures of all the previously discussed limiting cases as a function of the impurity-impurity distance. Oscillatory behavior in physical quantities is to be expected due to the generated Ruderman-Kittel-Kasuya-Yosida interaction. We are led to the conclusion that the well-known Doniach scenario captures essential aspects of this model, but the details, especially at small distances, are more complicated.