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The Mediterranean Sea hosts two subduction systems along the convergent Africa-Eurasia plate boundary that have produced strong ground shaking and generated tsunamis. Based on historical descriptions and sedimentary records, one of these events, in 365 CE, impacted a broad geographical area, including tsunami evidence for distances of 700–800 km from the source event, qualifying it as a ‘megatsunami’. Understanding how megatsunamis are produced, and where they are more likely, requires a better understanding of the different secondary processes linked to these events such as massive slope failures, multiple turbidity current generation, and basin seiching. Our sedimentary records from an extensive collection of cores located in distal and disconnected basins, identify turbidites which are analyzed using granulometry, elemental (XRF), micropaleontological, and geochemical data in order to reconstruct their coastal or marine source. The results show that the 365 CE basin floor sediments are a mixture of inner shelf and slope materials. The tsunami wave produced multiple far-field slope failures that resulted in stacked basal turbidites. It also caused transport of continent-derived organic carbon and deposition over basal turbidites and into isolated basins of the deep ocean. The composition of sediment in isolated basins suggests their deposition by large-scale sheet like flows similar to what has been caused by the Tohoku earthquake associated tsunamis. This is significant for rectifying and resolving where risk is greatest and how cross-basin tsunamis are generated. Based on these results, estimates of the underlying deposits from the same locations were interpreted as possible older megatsunamis.