Scanning tunnelling microscopy (STM) was used to follow Ostwald ripening, i.e. coarsening in two-dimensional molecular polycrystals directly on the molecular scale and in real time. For alkylated anthraquinone and oligothiophene different coarsening velocities have been found, and a two-dimensional reaction-controlled mechanism is proposed. Ostwald ripening is regarded as an intrinsic phenomenon of two-dimensional crystals at the solid-liquid interface,