Since the discovery of the H-mode in the ASDEX tokamak, many investigations of the phenomenon called ELMs (Edge-Localised Modes) have been made. ELMs are an instability associated with a rapid loss of particles and energy from the edge plasma. It is known that a temporal resolution in the ms range is necessary to resolve the fast changes during an ELM. However, hardly any investigation exists of the spatial fine structure of ELMs. We present here measurements with Langmuir probes and with a dedicated Ha fluctuation diagnostic in the edge and Scrape-Off layer (SOL) of the JET and "old" ASDEX tokamaks. It is our aim to demonstrate that ELMs display ane structure with very strong peaks in the fluctuating signals on the scale of ~1cm ^B, and of 10-50s duration. The signals from the main plasma edge are compared with signals from the divertor. In addition, estimates of the radial transport due to fluctuating E¥B uxes during ELMs are given for the case of JET.