The appearance and disappearance of H-mode behaviour in JET Tokamak discharges is associated with characteristic instabilities detected by edge magnetic probes, arrays of soft X-ray diodes and reflectometry: edge disruptive-like modes are observed before L-H transitions whereas H-L transitions are accompanied by large bursts of broad-band activity. Other observed fluctuations, shown to be resonant in the central region of the discharge, are not affected by the transitions. The importance of edge fluctuations and induced transport in a magnetic separatrix configuration is thus emphasised.