Rocks of Late Ordovician to Silurian age are well exposed on the western rim of the Murzuq Basin (Ghat-Tikiumit area, Libya) where seismic-scale exposures allow spectacular insights into the growth and decay of the Late Ordovician (Hirnantian) ice sheet. The final deglaciation left a complex topography with a combination of subglacial morphologies and proglacial depositional systems. This paper documents the glacial and proglacial palaeo-topography that controls the accumulation of a postglacial transgressive depositional system and the Rhuddanian (Early Silurian) shales. The glacial relief directly contributed to an important hiatus, with the Rhuddanian deposits at the base of the remnant glacial troughs being 3 Ma older than at the top of the topographic highs. The source-rock in the Murzuq Basin is of Early Rhuddanian age, so it is present only in the deepest part whereas geomorphic traps are formed within the highs of the relict postglacial topography. The transgressive system, recognised for its good reservoir potential, is considered to play a key-role in the petroleum system, linking the source rock deposited in the ancient topographic lows with the reservoir rocks in the topographic highs. This study aims to demonstrate the importance of palaeo-glaciological reconstructions for petroleum exploration of the Ordovician–Silurian in North Africa.