Various cell surface proteins, such as the B cell receptor (BCR) or immunoglobulin E bound to the membrane Type I RE receptor, possess two or more binding sites for soluble ligands which in turn have valences of three or more. We have devised an equilibrium model to calculate sizes and structures of cell surface aggregates formed between such species in two-dimensional systems directly from solution ligand concentration. The model explicitly treats differing ligand valences for different types of receptor-binding, monogamous bivalent binding of ligand-to-receptor and two-dimensional gelation of receptor-ligand aggregates. Of particular interest is that thermodynamic parameters reasonable for cell biological situations predict that two-dimensional receptor gelation can occur. This is the appearance of large aggregates (gel) in equilibrium with appreciable amounts of finite-sized aggregates (sol). Calculations also suggest (1) the amount of bound ligand increases with ligand concentration or ligand valence below the gel point, (2) the average number of receptors per finite aggregate increases with ligand concentration below the gel point, (3) finite aggregates generally involve less than two ligand molecules, (4) above the gel point, finite aggregate size remains approximately constant and bound ligand enters the gel-phase. Predicted gelation is also consistent with experiment. Polyvalent dinitrophenyl (DNP) antigens can aggregate bivalent DNP-specific BCR on cell or liposome surfaces. We have used the laser-microscopic method of fluorescence photobleaching recovery to examine the mobility of such protein aggregates both on B cells bearing DNP-specific BCR and on liposomal models. When either the DNP-antigen solution concentration or the number of DNP groups per antigen molecule exceeds a critical value, a fraction of the normally mobile bound antigen becomes immobile. At the same time, cells become resistant to antigenic and mitogenic stimulation. This suggests that two-dimensional gelation of antigen and BCR occurs with inhibition of subsequent BCR function. We discuss possible mechanisms by which large, immobile protein aggregates might inhibit cellular signaling systems, for example by slowing translocation of liganded receptor to lipid rafts.