Composite pressure sensitive hydrophilic adhesive, permeable for water vapor and losing its adhesivness in contact with liquid water, is particularly suitable for temporary glueing to the body surface for medical purposes. The composite is a gelled mixture of: (a) a water swellable, water insoluble polymer, soluble in polar water-miscible solvents boiling at atmospheric pressure at temperatures higher than 100 DEG C. as well as in their mixtures with minor amounts of water, (b) a hydrophilic water swellable polymer, insoluble in water as well as in polar water-miscible solvents boiling at atmospheric pressure at temperatures higher than 100 DEG C., and (c) a polar water-miscible innocuous solvent boiling at atmospheric pressure at temperatures higher than 100 DEG C., if desired mixed with a minor amount of water. A feature of the composite pressure sensitive hydrophilic adhesive of the invention is that the separate polymers (a) and (b) are replaced by a non-crosslinked copolymer of hydrophilic and hydrophobic monomers, only partially soluble in the component (c) but swellable therein.