Water-soluble terpolymers which contain, as copolymerized units,(a) from 10 to 35% by weight of an N-vinyllactam or an N-vinyl acid amide,(b) from 5 to 20% by weight of acrylic acid or of a salt of acrylic acid and(c) from 80 to 50% by weight of a C.sub.1 -C.sub.4 -alkyl vinyl ether,and have a glass transition temperature T.sub.g below 60.degree. C. can be prepared by polymerizing the monomer mixture in an inert organic solvent in the presence of a polymerization initiator and can, where appropriate, be partially or completely neutralized with a base, so as to form a salt. The products may be used as raw materials for adhesives or, in the form of an aqueous solution, as the adhesive itself.