A very general procedure entitled complete relaxation and conformational exchange matrix (CORCEMA) analysis has been developed to analyze the 2D-NOESY spectra of interacting systems undergoing multistate conformational exchange. This is an extension of earlier work from this laboratory on the methodological treatment of multistate conformational exchange [Krishna et al., Biopolymers 19, 2003 (1980)] and the theory of transferred NOESY for finite exchange off-rates [Lee and Krishna, J. Magn. Reson. 98, 36 (1992)]. The current theory is based on generalized rate matrices for relaxation and conformational exchange. The CORCEMA algorithm explicitly incorporates intermolecular dipolar cross relaxation between the molecules when they are complexed. It permits an analysis of NOESY intensities for the intra- as well as intermolecular contacts between the interacting molecules under a variety of binding conditions. Its application is illustrated on two examples of transferred NOESY simulations: (1) a two-state system involving a ligand and an enzyme forming a ligand-enzyme complex, and (2) a three-state system in which the ligand-enzyme complex can undergo a conformational transition from an "open state" to a "closed state," and can include conformational changes in both the complexed ligand and the complexed enzyme, such as hinge-bending motions. Simplifying expressions for generalized matrix analyses are derived for three limiting cases of the three-state system. This three-state example is illustrated using a hypothetical model of the hinge-bending motion in a thermolysin-inhibitor complex. It is shown that: (1) The neglect of cross relaxation between the interacting species in their complexed forms can lead to misleading conclusions on the "bound" conformation of the ligand. (2) If protein-mediated spin diffusion is dominant, caution is needed in analyses based on initial slopes alone due to one's inability to identify the exact range of the initial growth curve under poor signal/noise situations. (3) The neglect of conformational changes upon complexation, e.g., hinge-bending motions of the ligand-enzyme complex, can lead to erroneous results on the nature of "bound" conformations of the ligand. In this case, attempts to analyze the transferred NOESY data with a two-state model will result in a "virtual" conformation for the bound ligand. (4) When the hinge-bending rate is slower than the cross relaxation and enzyme off-rates, the bound conformation of a ligand deduced from the transferred NOESY experiment is more likely to represent nonspecific or weak binding in an open state of the enzyme.(ABSTRACT TRUNCATED AT 400 WORDS)