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Orbital forcing is a key climate driver over multi-millennial timescales. In particular, monsoon systems are thought to be driven by orbital cyclicity, especially by precession. Here, we analyse the impact of orbital forcing on global climate with a particular focus on the North African monsoon, by carrying out an ensemble of 22 equally spaced (one every 1000 years) atmosphere-ocean-vegetation simulations using the HadCM3L model, covering one full late Miocene precession-driven insolation cycle with varying obliquity (between 6.568 and 6.589 Ma). The simulations only differ in their prescribed orbital parameters, which vary realistically for the selected time period. We have also carried out two modern-orbit control experiments, one with late Miocene and one with present-day palaeogeography, and two additional sensitivity experiments for the orbital extremes with varying CO<inf>2</inf> forcing. Our results highlight the high sensitivity of the North African summer monsoon to orbital forcing, with strongly intensified precipitation during the precession minimum, leading to a northward penetration of vegetation up to ∼21° N. The modelled summer monsoon is also moderately sensitive to palaeogeography changes, but it has a low sensitivity to atmospheric CO<inf>2</inf> concentration between 280 and 400 ppm. Our simulations allow us to explore the climatic response to orbital forcing not only for the precession extremes but also on sub-precessional timescales. We demonstrate the importance of including orbital variability in model-data comparison studies, because doing so partially reduces the mismatch between the late Miocene terrestrial proxy record and model results. Failure to include orbital variability could also lead to significant miscorrelations in temperature-based proxy reconstructions for this time period, because of the asynchronicity between maximum (minimum) surface air temperatures and minimum (maximum) precession in several areas around the globe. This is of particular relevance for the North African regions, which have previously been identified as optimal areas to target for late Miocene palaeodata acquisition.