Non-local effects have recently been observed in many transient experiments in different tokamaks. These effects have been modelled by introducing a non-local dependence in the Bohm part of a previously introduced model for L-mode, so that good simulations are obtained for L - H transitions, cold pulses, sawteeth and ELMs. This model also explains the improvement of core transport in the whole high-performance phase of H-mode ELM-free discharges.