This study models the rainfall-runoff relationship in the Kebir-Rhumel River watershed in the Constantine Highlands, Algeria, using data from three concomitant rainfall and hydrometric stations. Statistical tests confirmed the absence of breaks in the series. We applied four conceptual models (GR4J, IHAC6, MORDOR, TOPMO8) and neural network models (RNN, NARX, LSTM) over three- and ten-year periods. Among the conceptual models, GR4J provided the best fit, highlighting the non-stationary nature of the relationship. The PMC neural network model performed well over three years but was less effective over ten years due to low flow influence. Notably, the NARX-RNN and RNN-LSTM models showed excellent predictive accuracy, with NARX-RNN perfectlycapturing flow dynamics and RNN-LSTM achieving minimal RMSE and high correlation coefficients.This study lies the comparative analysis of conceptual and neural network models, specifically the NARX-RNN and RNN-LSTM models, which have not been extensively applied in this context. This research fills the gap in understanding the effectiveness of neural network models in modelling non-stationary rainfall-runoff relationships in the region.