A Late Ordovician glacially related delta is documented based on architecture and facies from outcrops in the western Murzuq Basin (Libya). Sandstone megabeds highlight clinoform geometries of a proglacial, low-angle, shallow-water delta. The progradational wedge extends over 25 km from the SSE to the NNW and is about 100 m thick. Two types of clinothems have been distinguished, and eleven facies sequences are characterized in relation with their along-slope positions. Sand-prone facies sequences in type 1 clinothems relate to high-magnitude–low-frequency glacial outburst floods generating a freshwater, highly concentrated plunging hyperpycnal flow at the river mouth. During the waxing stage, the slope adjustment of an out-of-grade profile causes significant erosion. The resulting additional sediment charge involves along foresets a downslope flow transformation into a co-genetic sandy debris flow and high-density turbidity flow. Hybrid event beds including linked debrites and turbidites are the resulting deposits. In the lower slope, decreasing sediment concentration of the high-density turbidity flow leads to sediment lofting and to a second flow transformation resulting in a lower-density turbidity flow and a concomitant rising sediment plume. Deposition results in crude ripple cross-stratification. Debrite deposition is temporally restricted to an early segment of the rising limb of the flood hydrograph. During the ensuing waxing stage, uninterrupted, sustained-flow conditions maintain up to the peak flow, permitting the aggradation of thick sandstone successions with crude ripple cross-stratification. During the waning stage, backstepping of the whole depositional system leads to prevailing sedimentation in the delta-plain setting. Mouth-bar development and channel plugs are characterized by climbing-dune cross-stratification (CDCS). Shale-prone sedimentation in type 2 clinothems essentially corresponds to background ablation-related sedimentation but also includes minor, debrite-bearing, outburst-related event beds. This study documents the links between glacial outbursts, hyperpycnal flows, and hybrid beds in low-angle delta settings and illustrates a type of proximal, sand-dominated hyperpycnite. Dam failure of subglacial lakes is inferred for the outburst generation. Comparison with modern and Pleistocene examples may suggest that outburst events were days to several years in duration (type 1 clinothem), with a 1–40 ky recurrence period (type 2 clinothem).