Structurally viscous, curable, aqueous powder dispersions free entirely or substantially from organic solvents and comprising dimensionally stable particles (A) having an average particle size as measured by the laser diffraction method of D (v, 0.5)=1 to 10 .mu.m, the dimensionally stable particles (A) comprising as binder 10% to 100% by weight of at least one (meth)acrylate copolymer (A1) having an OH number of 40 to 250 mg KOH/g and an acid number of 5 to 100 mg KOH/g and prepared by multistage copolymerization of (a11) hydroxyl-containing acrylate and/or methacrylate monomers and (a12) acid-group-containing olefinically unsaturated monomers in organic solution, where (1) in one stage the entirety or predominant fraction of monomers (a11), if appropriate together with a small fraction of the monomers (a12), has been (co)polymerized, before (2) in a further stage the entirety or predominant fraction of monomers (a12), if appropriate together with the remainder of monomers (a11), has been co)polymerized; process for preparing them; and their use.