A problem related to the development of a supervised learning method for recurrent spiking neural networks is addressed in the paper. The widely used Leaky-Integrate-and-Fire model has been adopted as a spike neuron model. The proposed method is based on a known SpikeProp algorithm. In detail, the developed method enables gradient descent learning of recurrent or multi-layer feedforward spiking neural networks. The research included an extended verification study for the classical XOR classification problem. In addition, the developed learning method has been used to provide a spiking neural black-box model of fast processes occurring in a pressurised water nuclear reactor. The obtained simulation results demonstrate satisfactory effectiveness of the proposed approach.