Aqueous, structurally viscous powder dispersions curable by free-radical polymerization, substantially or entirely free from volatile organic compounds, and comprising as their disperse phase solid and/or highly viscous particles (A) which are dimensionally stable under storage and application conditions and have a z-mean average particle size as measured by photon correlation spectroscopy of 80 to 750 nm, the particles (A) comprising at least one free-radically crosslinkable binder (A1) having a glass transition temperature of -70 to +50.degree. C., an olefinically unsaturated double bond content of 2 to 10 eq/kg and an acid group content of 0.05 to 15 eq/kg, in an amount, based on (A), of 50 to 100% by weight; process for their preparation, and their use.