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Summary: A mathematical theory of competitive labelled-ligand assays was developed with the intention of theoretically re-evaluating the optimal assay conditions and precision data of assay Systems established by experiment. Our theory is based upon the assumptions of a simple bimolecular reaction mechanism, homogeneous reactants, as well as kinetically indistinguishable labelled and non-labelled ligands. The general case of two-step (non-equilibrium) assay was considered including the one-step (equilibrium) assay as a special case. The solution of the System of corresponding kinetic differential equations was used to mathematicall y construct Standard curves. Furthermore, intraassay precision profiles and indices as well as detection limits were calculated considering solely the pipetting error, , as a source of experimental error. A procedure was outlined to mathematicall y determine the optimal incubation conditions for any assay System targeted to a given analyte concentration, P, at which the Standard deviation of assay results is to be minimized. Estimates of both the content of binding sites and the equilibrium constant, K, of the specific binding agent are necessary, and these can be derived from Scatchard plots. For six RIA Systems, of which three were one-step and three were two-step assays, experimental assay conditions and precision data were compared with theoretical predictions. Experimentally determined antibody binding site concentrations agreed fairly well with those independently evaluated by mathematical optimization. Mean precision indices, defined as constituting an average over the complete precision profile, were fotind to be within the theoretically predicted range, i. e. two- to threefold the pipetting error. Detection limits (Standard deviation near concentration 0) differed from theoretical values at most by a factor of two in the case of two-step assays and were nearly identical with theoretical values for one-step assays. Generally, they were Of the order of , approaching a lower limit by the order of , when P falls to the order of K. Comparing the advantages of the one-step and two-step technique of competitive labelled ligand assays, the following results were obtained: The one-step method provides a more favourable pfecision profile, especially a better detection limit, and a higher specificity of analyte recogiution. The quantity of reagents needed (specific binding agent as well as labelled ligand) is three to four times lower than in the two^step method. On the other hand, the higher amount of reagents employed for the two-step technique results in a considefably higher measuring signal, which is important where activity of the labelled ligand is low. We conclude that mathematical modelling of labelled-ligand assays should be useful in re-evaluating assay conditions and precision data obtained by experiment. Furthermore, it permits some general assertions concenung the principal limits of assay precision as well as the advantages and disadvantages pf different assay protocols.