There are some techno-typological features of the lithic assemblages traditionally associated with the emergency and affirmation of the Upper Palaeolithic (in Europe and Asia) or Later Stone Age (Africa). Among them a particular attention have gained, in the Lower LSA of Libya, the so-called “chamfered pieces” or “chamfrein”. Since their discovery, in the mid-fifties, by Charles McBurney, they have been directly associated with the ones found in the Upper Palaeolithic layers of Ksar Akil Cave, in Lebanon. This association led, in the past, to the development of a diffusionist hypothesis, suggesting the arrival in North Africa of a proper “Upper Palaeolithic” culture from the Near East. This paper offers a critical revision of the technological features of the chamfered pieces and their role within the lithic assemblages of Ksar Akil, on one side, and Haua Fteah, on the other. This will allow to reconsider the hypothesis of a local development in Libya of the Later Stone Age and to evaluate the possible role of a cultural convergence.