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A simple theoretical model for the antigen--antibody reaction is presented and used to evaluate the optimum conditions for designing solid phase radioimmunoassays (RIA) using labelled antibodies. Both theoretical and experimental data are presented, using a wide variety of antigens and their corresponding antibodies. The types of RIA described include the direct, the indirect, the direct sandwich assays for detecting either antigen or antibody. The experimental results confirm in a semiquantitative manner that the greatest sensitivity of the RIA is achieved when the smallest amount of labelled antibody is used, that whenever possible the antigen/antibody ratio should be greater than unity ( >1 ), and that the formation of the antigen--antibody complex is dependent on the mass action effect.