Enzymes often show catalytic allostery in which reactions occurring at different sites communicate cooperatively over distances of up to a few nanometres. Whether such effects can occur with non-biological nanocatalysts remains unclear, even though these nanocatalysts can undergo restructuring and molecules can diffuse over catalyst surfaces. Here we report that phenomenologically similar, but mechanistically distinct, cooperative effects indeed exist for nanocatalysts. Using spatiotemporally resolved single-molecule catalysis imaging, we find that catalytic reactions on a single Pd or Au nanocatalyst can communicate with each other, probably via hopping of positively charged holes on the catalyst surface, over ~102 nanometres and with a temporal memory of ~101 to 102 seconds, giving rise to positive cooperativity among its surface active sites. Similar communication is also observed between individual nanocatalysts, however it operates via a molecular diffusion mechanism involving negatively charged product molecules, and its communication distance is many micrometres. Generalization of these long-range intra- and interparticle catalytic communication mechanisms may introduce a novel conceptual framework for understanding nanoscale catalysis.