Crosslinked copolymers wherein crosslinking is effected with crosslinking bridge members of the formula ##STR1## wherein R.sup.1 and R.sup.2 independently of one another are each hydrogen or alkyl with 1 to 4 carbon atoms and m represents a number from 0 to 6 are prepared by copolymerization of monomers with vinylphosphonic acid (ester)-anhydrides and the new crosslinked polymers according to the invention are suitable for the preparation of acid-soluble coatings and encapsulation materials.