Extreme value theory becomes increasingly important for hydrologists in order to assess the hazard related to extreme rainfall and ooding. The annual maximum daily precipitation at one site is often modelled with a GEV distribution[1]. The objective of the present study is to describe the extreme rainfall in French Mediterranean region with dierent covariate models[2]. 92 precipitation gauges within this region are utilized. Based on dierent covariates (like time, weather type and climate indices) and regression models (e.g. linearity on location parameter, scale parameter or both), several non-stationary GEV models are constructed. The Bayesian approach and the Markov chain Monte Carlo (MCMC) methods are used to infer the posterior parameter distributions[1], to assess uncertainties and to examine the performance of dierent probability models. Moreover, the predictive distributions are computed to make predictions on future observations. Due to the limited information content of at-site data, the identication of at-site non-stationary models becomes challenging. The construction of a general modelling framework for regional non-stationary models will thus be discussed.