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Rainfall intensity-duration-frequency (IDF) curves are commonly used for the design of water resources infrastructure. Numerous studies reported non-stationarity in meteorological time series. Neglecting to incorporate non-stationarities in hydrological models may lead to inaccurate results. The present work focuses on the development of a general methodology that copes with non-stationarities that may exist in rainfall, by making the parameters of the IDF relationship dependent on the covariates of time and climate oscillations. In the recent literature, non-stationary models are generally fit on data series of specific durations. In the approach proposed here, a single model with a separate functional relation with the return period and the rainfall duration is instead defined. This model has the advantage of being simpler and extending the effective sample size. Its parameters are estimated with the maximum composite likelihood method. Two sites in Ontario, Canada and one site in California, USA, exhibiting non-stationary behaviours are used as case studies to illustrate the proposed method. For these case studies, the time and the climate indices Atlantic Multi-decadal Oscillation (AMO) and Western Hemisphere Warm Pool (WHWP) for the stations in Canada, and the time and the climate indices Southern Oscillation Index (SOI) and Pacific Decadal Oscillation (PDO) for the stations in United States are used as covariates. The Gumbel and the generalized extreme value distributions are used as the time-dependent functions in the numerator of the general IDF relationship. Results show that the non-stationary framework for IDF modelling provides a better fit to the data than its stationary counterpart according to the Akaike information criterion. Results indicate also that the proposed generalized approach is more robust than the common approach especially for stations with short rainfall records (e.g., R-2 of 0.98 compared to 0.69 for duration of 30 min and a sample size of 27 years).