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The paper presents new methods for modelling of temperature sensors' dynamics by means of Artificial Neural Networks (ANN) and hybrid analytical-neural approach. Feedforward multilayer ANN and a moving window method, as well as Recurrent Neural Networks (RNN) are applied. The proposed modelling techniques were evaluated experimentally for two small platinum Resistance Temperature Detectors (RTDs) immersed in oil. Experiments were performed in temperature range, for which the sensors characteristics are nonlinear. The proposed ANN-based and hybrid analytical-neural models were validated by means of computer simulations on the basis of the quality of dynamic errors correction. It was shown that in the process conditions for which classical methods and linear models fail, the application of ANNs and hybrid techniques which combine soft and hard computing paradigms can significantly improve modelling quality.