A redispersible polymer powder has very polyvalent uses, for example in hydraulic setting systems, but also as binder for the most different applications, and can be produced by spray drying aqueous dispersions. The sprayable aqueous dispersions are prepared by mixing an aqueous polymer dispersion 1 (containing polymer I) with an aqueous polymer dispersion 2 (containing polymer II). The diameter of the particles of polymer I is 5 to 150 times, preferably 15 to 50 times larger than the diameter of the particles of polymer II. Polymer I is a film-forming polymer at room temperature while polymer II has a higher glass transition temperature than polymer I, is water-insoluble and therefore is undissolved in the aqueous dispersion to be sprayed. These polymer powders are characterised by a distinctly improved block strength and very good storage stability.