Water-redispersible polymer powder compositions with accelerated-setting action based on homo- or copolymers of one or more monomers of vinyl esters of optionally branched C.sub.1-15 alkylcarboxylic acids, (meth)acrylic esters of C.sub.1-15 alcohols, vinylaromatics, olefins, dienes, and vinyl halides, one or more protective colloids, and optionally antiblocking agent(s), contain one or more setting-accelerants NR.sub.3, R.sub.2N--(CH.sub.2).sub.n--NR.sub.2, or one or more singly or doubly NH.sub.2-terminated polyalkylene glycols having a C.sub.1-C.sub.6-alkylene group is/are present, where n=from 1 to 4, and where the radicals R are identical or different, and are hydrogen, a C.sub.1-C.sub.6-alkyl radical, or a C.sub.1-C.sub.6-hydroxyalkyl radical, where at least one radical R is a C.sub.1-C.sub.6-hydroxyalkyl radical, and wherein the setting-accelerants may optionally be present in the form of their salts.