The bienzyme conjugate (SOD-CHS-CAT) of superoxide dismutase and catalase (covalently coupled with each other through chondroitin sulfate, a glycosaminoglycan of the endothelial glycocalyx) was assayed with respect to its vasoprotective activity in interaction with platelets and the rat arterial ring, and in normalization of the hemodynamic parameters in rats and rabbits pathologically altered by exposure to hydrogen peroxide to simulate the development of oxidative stress. The SOD-CHS-CAT conjugate has anti-platelet potential owing to the antiaggregatory effect of the combined enzymatic activities and the supramolecular structure acquired. The effect of SOD and CAT on arterial ring tonus was equivalent for both their native and conjugated forms. The normalizing effect of the SOD-CHS-CAT conjugate on blood arterial pressure and heart rate (after their perturbation by hydrogen peroxide) in rats and rabbits was significantly more effective than the control values. The study demonstrates the possibility of using the SOD-CHS-CAT conjugate in chronic prophylactic therapy and the feasibility of developing oral forms of the conjugate. These features of the SOD-CHS-CAT conjugate, its good tolerability and satisfactory acute toxicity, qualify this product as promising drug candidate, suggesting a versatile approach for developing enzyme conjugates for medical needs.