What is described is a reactive extrusion process of making a polymeric hydrogel of a polymeric anhydride or acid, e.g. maleic anhydride or maleic acid polymer, or copolymer thereof, crosslinked with a crosslinking agent containing at least 2 crosslinkable groups, particularly, —OH or —NH2, or both. The reaction product is a crosslinked polymeric ester or amide/imide, or both, suitably having a mole ratio of —OH, or —NH2, to —COOH, of 1:10 to 10:1, preferably 2:10 to 7:1. The hydrogel is particularly swellable in water, e.g. >100% in 1 hour in aqueous media; and forms a thin, tacky layer on a substrate, which property is useful in bioadhesive products.