Abstract A simulation of two-site immunoradiometric assays (2-site IRMA) based on calculations of chemical equilibria was derived and used to investigate assay conditions under which aberrant results may occur. In simulated 2-site IRMA, the assay response was governed in a complicated but predictable way by (i) the amount of analyte immobilized by the solid-phase antibody in the first step of the assay, (ii) the extent of competing side reactions in the second step of the assay, and (iii) the extent of complexing of immobilized analyte by labeled antibody in the second step of the assay. This last determinant of assay response was particularly important when inadequate concentrations of labeled antibody were present in the second step of the assay. Under these conditions a fall in the assay response occurred at high sample concentrations. This previously reported artefact, known as the “hook effect”, could thus be produced in simulated assays without assuming that the solid-phase antibody was contaminated with low-affinity binding sites or that incomplete washing of the solid phase occurred after the first assay step.