AbstractSediment accumulation within ocean trenches located at actively accreting convergent margins is determined by an interplay between sediment supply, sediment subduction/accretion at the toe of the overriding accretionary complex and the rate of subduction. Modelling trench sedimentation provides insight into the principal controlling factors, and a means of deriving, from the pattern of sedimentation, how factors, such as the rates of sediment supply and subduction, have varied over the period of accumulation of the trench sediments. Two DSDP‐ODP drill sites within the Nankai Trough reveal a coarsening‐upward megasequence, indicating a progressive facies transition from abyssal muds to outer‐trench silts to inner‐trench sands. The changing geometry of the trench‐wedge over the past 1 Myr has been determined by modelling variations in net sediment flux for two trench‐perpendicular profiles. The models were constrained to fit the stratigraphy at the drill sites, and the simulated present‐day geometries of the trench were matched with those shown on seismic reflection profiles by successive adjustment of the model. Results from both sites confirm a ‘slow’ subduction rate of<20 km Myr‐1. At the south‐western site (582), the width of the trench‐wedge has ranged from 13 to 21 km over the past 1 Myr. To the north‐east, at Site 808, the width has ranged from 7 to 13 km over the past 0.5 Myr. These changes in trench‐wedge width are primarily the result of large changes in sediment supply rate. The subduction of the Shikoku Ridge, a fossil spreading centre adjacent to Site 808, has had a major influence on the style of sedimentation within the trench.The style of accretion from the trench to the toe of the accretionary complex has important implications for geometrical adjustment of the trench‐wedge. Thrust displacement lifts the protothrust region out of the trench, resulting in a decreased width. This is followed by a phase of increasing width as the trench‐wedge adjusts towards a new equilibrium. The cyclical, episodic accretion process results in a periodic second‐order variation in trench‐fill size that is superimposed on primary trends determined by variations in sediment supply r