Hydroxamic acid polymers which are comprised of hydroxamic groups and carboxylic acid groups wherein the carboxylic acid groups constitute less than about 3% of the functional groups. The polymers hereof are also especially useful in biomedical applications because, for example, the low concentration of carboxylic acid groups decreases the incidence of bioincompatibility. Additionally, the polymers exhibit anticoagulant activity, urease inhibition activity, metal chelating activity and ion exchange activity.