A competitive low-affinity binding model was proposed for determining the number of mutual (overlapped) and specific binding sites of two ligands (A, B) on a protein (P). To use the model, one needs to carry out a titration experiment by adding either ligand A or B into a three-component system (A-B-P), and to monitor the spectroscopic parameter changes. Fitting the titration curve to the proposed model, one can get the mutual and specific binding sites of the two ligands on the protein. The model was examined by using human serum albumin (HSA) as a receptor and tolmetin (TOL) and salicylic acid (SAL) as ligands. Proton longitudinal relaxation rates (R1) were measured on a 500-MHz NMR spectrometer during the titration and used to derive the mutual binding sites. It was found that among the binding sites of 32+/-4 for SAL and 28+/-2 for TOL on HSA, there were 17+/-5 mutual sites for the two ligands. This result indicates that, although HSA has large binding capacities for most ligands, there are still a reasonable amount of the low-affinity binding sites that are structure selective.