The invention provides an adhesive with an aqueous polymer dispersion. The aqueous polymer dispersion comprises a copolymer of a) esters of vinyl alcohol with C2 to C6 monocarboxylic acids, b) α,β-unsaturated C3 to C9 carboxylic acids or vinyl-substituted phosphonic or sulfonic acids, c) polyunsaturated monomers, and optionally d) non-polar, copolymerizable monomers and e) copolymerizable monomers that carry polar functional groups, where the ratio of c:b ranges from 1:10 to 1:400. The adhesive has high adhesion strength, stable viscosity during high-speed automatic application process and, is optionally, remoistenable with water or becomes water-soluble. The adhesive may be advantageous used as wood adhesive, remoistenable adhesive, label adhesive, bottle adhesive, and the like.