A polymeric composition that generates nitric oxide and a process for rendering the surface of a substrate nonthrombogenic by applying a coating of the polymeric composition to the substrate are disclosed. The composition comprises: (1) a crosslinked chemical combination of (i) a polymer having amino group-containing side chains along a backbone forming the polymer, and (ii) a crosslinking agent containing functional groups capable of reacting with the amino groups; and (2) a plurality of nitric oxide generating functional groups associated with the crosslinked chemical combination. Once exposed to a physiological environment, the coating generates nitric oxide thereby inhibiting platelet aggregation. In one embodiment, the nitric oxide generating functional groups are provided by a nitrated compound (e.g., nitrocellulose) imbedded in the polymeric composition. In another embodiment, the nitric oxide generating functional groups comprise N₂O₂^- groups covalently bonded to amino groups on the polymer.