Résumé : In Evolutionary Robotics, auto-teaching networks, neural networks that modify their own weights during the life-time of the robot, have been shown to be powerful architectures to develop adaptive controllers. Unfortunately, when run for a longer period of time than that used during evolution, the long-term behavior of such networks can become unpredictable. This paper gives an example of such dangerous behavior, and proposes an alternative solution based on anticipation: as in auto-teaching networks, a secondary network is evolved, but its outputs try to predict the next state of the robot sensors. The weights of the action network are adjusted using some back-propagation procedure based on the errors made by the anticipatory network. First results -- in simulated environments -- show a tremendous increase in robustness of the long-term behavior of the controller.