This paper presents the design of a nonlinear robust observer for the estimation of the neutron precursor power and internal reactivity in a nuclear research reactor when only the input and the neutron power are available for measurement. The observer is based on a differential neural network with internal and external layers. Besides, this observer has two correction terms: Luenberger one and sliding mode one. This last term is intended to reduce the output external noise effect. The neural network is initially trained off-line using a very simplified third order nonlinear model of the nuclear reactor. The off-line training process is robust with respect to the model employed. Thus, when this preliminary training has finished, the neural observer can work as a completely physical model-free system and can carry out the on-line state estimation within a small margin of error despite uncertainty and noise. The efficiency of this technique with a guaranteed bound for the averaged estimation error is illustrated by simulation.