JET plasmas are affected by various instabilities, which can be particularly dangerous in high performance discharges. An identification method, based on the use of advanced neural networks called Recurrent Neural Networks (RNNs), has been applied to ELMs and sawteeth. The approach is. The potential of the recurrent networks to identify the dynamics of the instabilities has been first tested using synthetic data. The networks have then been applied to JET experimental signals. An appropriate selection of the networks topology allows identifying quite well the time evolution of the edge temperature and of magnetic fields, considered the best indicators of the ELMs. A quite limited number of periodic oscillations are used to train the networks, which then manage to follow quite well the dynamics of the instabilities, in a recurrent configuration on one of the inputs. The time evolution of the aforementioned signals, also during intervals not used in the training and never seen by the networks, are properly reproduced. A careful analysis of the various terms in the RNNs has the potential to give clear indications about the nature of these instabilities and their dynamical behaviour.