We demonstrate far-field fluorescence microscopy with subdiffraction resolution of rapidly moving nanoparticles. Fast recording on the nanoscale is accomplished by merging rapid beam scanning with stimulated emission depletion (STED) microscopy. By recording at 80 frames per second with a focal spot area which is 9-10-fold smaller than the diffraction limit, the Brownian motion of a dense suspension of 36 nm particles was revealed. Individual particles were localized with ~20 nm accuracy, while automated particle tracking revealed their distribution of speeds. The first combination of rapid image acquisition with a diffraction-unlimited far-field microscopy concept heralds a large range of possible applications of dynamic fluorescence nanoscopy in various fields, including in biology.