Cell adhesion provides not only physical linkage but also communication between the cell and its environment. As such, it is important to many cellular functions. Recently, the probability distribution of forming a low number of specific adhesive bonds in a short-duration contact has been described (Chesla et al., Biophys. J. , 1998, 75:1553-1572). This model assumes that binding occurs between a single receptor species and a single ligand species. However, cell adhesion molecules rarely work alone in physiological settings. To account for these in vivo situations, we extended the previous model to include concurrent interactions of multiple receptor-ligand species, introducing the concept of independent binding. Closed-form solutions have been obtained for cases where competition is absent or can be neglected. In two companion papers (Williams et al., Biophys. J., 2000, 79:1858-1866; 2000, 79:1867-1875), the model developed herein has been applied to analyze two sets of experiments designed such that the validity of the theory was also tested.