Polymers having non-thrombogenic properties can be prepared by copolymerizing monomers of at least three classes selected from (a) monomers having sulphate groups, (b) monomers having sulphonate groups, (c) monomers having sulphamate groups, (d) monomers having polyoxyalkylene ether groups, and (e) monomers having zwitterionic groups. The polymers can additionally be provided with anti-thrombogenic properties by including an additional comonomer having a pendant heparin (or hirudin, warfarin or hyaluronic acid) group. The polymers can be used as coating materials for medical devices, such as tubing or connectors, in order to provide them with non-thrombogenic, and optionally anti-thrombogenic, properties.