DSS1 and DSS2 are two oversulfated dermatan sulfate derivatives with sulfur contents of 7.8% and 11.5%, respectively. DSS1 and DSS2 both enhanced the rate at which antithrombin (AT) inactivates thrombin according to a concentration dependent manner. The analysis of the experimental data, using our previously described kinetic model [Biomaterials1997, 18, 203] (i) suggested that both DSS1 and DSS2 catalyzed the thrombin-AT reaction according to a mechanism in which the oversulfated derivative quickly formed with AT a complex, which was more reactive towards thrombin than the free inhibitor and (ii) allowed us to determine the dissociation constants of the polysaccharide-inhibitor complexes, which were (1.15 +/- 0.74) x 10(-7) and (7.17 +/- 0.65) x 10(-9) M, and the catalyzed reaction rate constants, which were (2.29 +/- 0.15) x 10(8) and (8.71 +/- 0.08) x 10(8) M(-1) min(-1), for DSS1 and DSS2, respectively. These data suggested that the oversulfation confers an affinity for AT to dermatan sulfate and that the higher the sulfur content the higher the affinity for AT. They also suggested that the reactivities of the polysaccharide-AT complexes formed towards the protease increased with the sulfur content.