Two models of immunoadsorbent assays are developed that describe the competitive adsorption of labeled antigen and unlabeled analyte to antibody binding sites immobilized on a solid surface. In the first model, a small labeled antigen and a small unlabeled analyte compete with only binding site limitations and no steric limitations. A multicomponent Langmuir isotherm results that is sufficient to quantify competitive adsorption. This model can describe, with no adjustable parameters, the data of competitive assays for biotin using biotinylated horseradish peroxidase (B-HRP) over a wide range of anti-biotin antibody (ABA) surface densities. In the second model, the small unlabeled analyte competes with a large colloidal particle containing many antigens and enzyme labels attached to its surface. This model quantifies the steric interference that large particles can experience upon binding (large ligand effect) due to the lower probability of finding an available area of the right size to accommodate the larger adsorbent. This large ligand model also takes into account the increased probability of binding a large particle due to the larger number of antibody binding sites covered per collision. The resulting model is used to analyze the competitive assay data of biotin competing with liposomes to which many biotin and HRP molecules have been conjugated. This analysis is of interest because previous work has shown that these bifunctional liposomes can reduce the detection limit for antigens in bulk solution relative to assays performed with conventional small labeled antigens.