The kinetics of cAMP hydrolysis by the purified calf liver cGMP-stimulated cyclic nucleotide phosphodiesterase were analyzed in the absence or presence of a number of competitive inhibitors of the methylxanthine type according to a two-site competitive model for allosteric enzymes. Methylxanthines were also classified by graphical analysis of classical competition kinetics at saturating cAMP. This treatment yielded Km/KI ratios which estimated the relative effectiveness of the binding of substrate and inhibitors to the "high affinity" (ES complex) state without establishing individual equilibrium-binding constants of cAMP and inhibitors for specific enzyme states. Individual binding constants for substrate and inhibitors were estimated directly by fitting primary data to the rate equation for the two-site competitive model. The equilibrium dissociation constants for cAMP to the "high" (KS) and "low affinity" (AKS) states were 2.4 +/- 0.8 and 410 +/- 140 microM, respectively. Dissociation constants for various inhibitors to the high (BKI) and low affinity (KI) states were also estimated. The ratio KS/BKI, which directly compared the equilibrium-binding constants of substrate and inhibitors to the high affinity state (ES complex), was in excellent agreement with Km/KI ratios derived from graphical analysis. Whereas a number of the methylxanthine analogues were more effective or as effective as cAMP in binding to the low affinity or "ligand-free" state, only isobutylmethylxanthine was effective as cAMP in binding to the high affinity state (1-methyl-3-isopropylxanthine, and 1,3-dipropylxanthine were somewhat less effective). These findings suggested that allosteric transitions might alter the topography of specific hydrophobic domains at cyclic nucleotide-binding sites and that structural determinants were more stringent for binding to the high affinity state than to the low affinity state.