While the oil currency property is clearly established from a theoretical viewpoint, its existence is less clear-cut in the empirical literature. We investigate the reasons for this apparent puzzle by studying the time-varying nature of the relationship between real effective exchange rates of five oil exporters and the real oil price in the aftermath of the oil price shocks of the last two decades. Accordingly, we rely on a time-varying parameter VAR specification which allows the responses of real exchange rates to different oil price shocks to evolve over time. We find that the reason of the mixed results obtained in the empirical literature is that oil currencies follow different hybrid models in the sense that oil countries' real exchange rates may be driven by one or several sources of oil price shocks that furthermore can vary over time. In addition to structural changes affecting oil countries, structural changes arising from the oil market itself through the various, time-varying sources of oil price shocks are found to be crucial.