Depending on the task of a decision-support system, the underlying computer simulation can be carried out in real time or faster than real time. The required high simulation speed is a major obstacle in employing the more advanced simulation models. The work addresses the question of the recurrent neural network (RNN) usage for the faster than real-time simulation of hydraulic systems. Mathematical models of such systems are computationally expensive for numerical integration due to their high non-linearity and numerical stiffness. In this paper, a mathematical-based simulation model has been created using an experimentally verified mathematical model of a hydraulic position servo system (HPS). A RNN of the NARX architecture has been developed, trained and tested on the training data produced by the mathematical-based simulation model. A preprocessing technique has been developed and applied to the training data in order to speed-up the training and simulation processes. The obtained results for the first time show that the employment of the RNN together with the developed preprocessing technique ensures the simulation speed-up of the complex hydraulic system at the expense of a small accuracy decrease. In the considered case of the HPS, a simulation speed-up of factor 4.8 has been obtained.