Compositions and methods are provided for preventing formation of thrombosis on a liquid-contacting surface of a liquid delivery system, such as a port, catheter or port-catheter system. The liquid delivery system is connected to a patient for delivery of a liquid to the patient. The method involves contacting the surface with a thrombosis-preventing liquid containing taurolidine, taurultam or a mixture thereof, the thrombosis-preventing liquid further containing an anticoagulant agent. In an alternative embodiment, the liquid-contacting surface of the delivery system is contacted with a solution containing an anticoagulant agent, and thereafter contacted with a solution containing taurolidine, taurultam or a mixture thereof.