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In tectonically active mountain ranges, landslides triggered by earthquakes mobilise large volumes of sediment that affect river dynamics. This sediment delivery can cause downstream changes in river geometry and transport capacity that affect the river efficiency to export this sediment out of the epicentre area. The subsequent propagation of landslide deposits in the fluvial network has implications for the management of hazards downstream and for the long-term evolution of topography over multiple seismic cycles. A full understanding of the processes and time scales associated with the removal of landslide sediment by rivers following earthquakes however, is still lacking. Here, we propose a nested numerical approach to investigate the processes controlling the post-seismic sediment evacuation at the mountain range scale, informed by results from a reach scale model. First, we explore the river morphodynamic response to a landslide cascade at the reach-scale using a 2D modelling approach. The results are then used to describe empirically the evacuation of a landslide volume which avoids using a computationally extensive model in catchments which may have thousands of co-seismic landslides. Second, we propose a reduced-complexity model to quantify evacuation times of earthquake-triggered landslide clusters at the scale of a mountain range, examining the hypothetical case of a M w 7.9 earthquake and its aftershocks occurring on the Alpine Fault, New Zealand. Our approach combines an empirical description of co-seismic landslide clusters with the sediment export processes involved during the post-seismic phase. Our results show that the inter-seismic capacity of the mountain range to evacuate co-seismic sediment is critical to assess the sediment budget of large earthquakes, over one to several seismic cycles. We show that sediment evacuation is controlled by two timescales, 1. the transfer time of material from hillslopes to channels and 2. the evacuation time of the landslide deposits once it has reached the fluvial network. In turn, post-seismic sediment evacuation can either be connectivity-limited, when sediment delivery along hillslopes is the main limiting process, or transport-limited, when the transport by rivers is the limiting process. Despite high values of runoff, we suggest that the Southern Alps of New Zealand are likely to be in connectivity-limited conditions, for connection velocities <10 m.yr−1. Connection velocities >2 m.yr−1 are sufficient to allow most of co-seismic sediments to be mobilised and potentially exported out of the range within less than one seismic cycle. Because of the poorly-constrained rate of sediment transfer along hillslopes, our results potentially raise the issue of co-seismic sediment accumulation within mountain ranges over several seismic cycles and of the imbalance between tectonic inputs and sediment export. We, therefore, call for renewed observational efforts to better describe and quantify the physical processes responsible for the redistribution and mobilization of sediment from landslide scars and deposits. [ABSTRACT FROM AUTHOR]