Dynamical systems are often considered immune from memory effects, the dependence of evolution from the previous history. This hypothesis has been tested for two phenomena in nuclear fusion, which are believed to sometimes show sensitivity to the previous evolution of the discharge: disruptions and the transition from the L to the H mode of confinement. To this end, two innovative neural network architectures, the Tapped Delay Lines and the Recurrent Networks of the Elman type, have been applied to JET database to extract these potential memory effects from the time series of the available signals. Both architectures can detect the dependence from the past history quite effectively. In the case of disruptions, only the ones triggered by locked modes seem to be influenced by the past history of the discharge. With regard to the L-H transition, memory effects are present only in the time interval very close to the transition, whereas, once the plasma has settled down in one of the two regimes, no evidence from the previous evolution has been detected.