Novel conjugates of glycosaminoglycans, particularly heparin and dermatan sulfate, and amine containing species and therapeutic uses thereof are described. In particular, mild methods of conjugating heparins to proteins, such as antithrombin III and heparin cofactor II, which provide covalent conjugates which retain maximal biological activity are described. Uses of these conjugates to prevent thrombogenesis, in particular in lung airways, such as found in infant and adult respiratory distress syndrome, and on surfaces in contact with blood are also described.