A process for producing a polymer powder comprising vinylformamide units by free radical polymerization of an aqueous solution of N-vinylformamide and if appropriate other monomers and drying the polymer which comprises an aqueous monomer solution comprising N-vinylformamide and at least one polymerization initiator being spray dispensed as an aerosol or dropletized at the top of a heatable tower-shaped reactor, then polymerizing the aerosol or droplets in an inert gas atmosphere to form a finely divided solid and discharging the finely divided polymer from the reactor.