Theory is formulated using reacted-site probability functions to relate the concentration of monomer to that of total solute for a multivalent monomer which undergoes indefinite self-association to form an equilibrium array of linear chains and branched networks governed by a single site-binding constant. In turn, this intrinsic constant is related to the stoichiometric equilibrium constants describing successive additions of monomer; and the characterization of the composition of the mixture at different total concentrations is discussed together with the onset of gelation, which occurs when each polymer (excluding the infinite network) attains a maximum concentration. Analogous expressions defining solution composition are presented for indefinitely self-associating systems involving non-identical sites when interactions occur in a head-to-tail fashion between dissimilar sites. Finally, a bivalent monomer is considered with head-to-head and tail-to-tail interactions forming an indefinite array of polymers with alternating bond types. It is shown that the latter description is quantitatively consistent with results obtained previously on the indefinitely self-associating zinc-free insulin system. The postulated self-association pattern involving two site-binding constants of magnitudes 5.75 X 10(4) M-1 and 0.85 X 10(4) M-1 is preferred to earlier suggested models on the basis of information available from X-ray crystallographic studies on insulin.