Difficulties are encountered in the thermodynamic characterization of interactions between a protein ligand and a linear acceptor, such as a polynucleotide or a polysaccharide, because of the involvement of more than one unit of the polymer chain in each attachment of a protein molecule. Complications arise from the fact that random attachment of ligand to the polymer chain, each unit of which is a potential binding site, initially leads to suboptimal location of protein molecules along the polymer chain-a situation that has to be rectified before the attainment of thermodynamic equilibrium can be realized. Kinetic as well as thermodynamic consequences of such nonspecific binding, termed the parking problem, therefore need to be considered in any quantitative characterization of the interaction between a large ligand and a linear polymer acceptor chain. Results for the thrombin-heparin interaction have been used to illustrate a thermodynamic characterization of nonspecific binding that takes into account these consequences of the parking problem.