A method for preparing hydroxamic acid polymers from primary amide polymers wherein polyvinyl monomers such as polyacrylamide are reacted with hydroxyl amine in aqueous solution at room temperature. The low reaction temperature is crucial to producing a high yield (70%) of polymer with hydroxamic acid groups and having a low carboxylic acid content (less than 15%, preferably less than 3%). The polymers display high metal affinity over a broad pH range.The polymers are particularly useful for biomedical applications due to the low carboxylic acid content and for the removal and purification of metals due to the high binding constants and rapid reaction rates.