Thrombus or clot formation and accretion are inhibited by administering thrombin-displacing substances to a patient. The thrombin-displacing substances comprise either thrombin analogs which bind to the thrombin-binding site on fibrin or fibrin analogs which bind to a fibrin-binding site on thrombin. By displacing the thrombin from clot or thrombus, the thrombin is released into circulation where it is inactivated by endogenous anti-proteinases. The fibrin analogs which bind to the fibrin-binding site on thrombin may be linked to a second binding moiety which binds to and/or inactivates the catalytic site and/or exosite I on thrombin to further inhibit thrombosis. The ability of test substances to displace thrombin is measured by exposure of the substance to immobilized thrombin-fibrin complex.