The Los Sombreros Formation represents the western continental margin slope deposits of the Argentine Precordillera, a sub-terrane accreted to Gondwana as part of the Cuyania Terrane in early Palaeozoic times. The age of these gravity-driven deposits is controversial and, therefore, a precise biostratigraphic scheme is essential to reveal the evolution of the continental margin. New conodont samplings along with sedimentological and structural analysis carried out in the Los Sombreros Formation in the La Invernada Range provide clues to its depositional framework. The sedimentary succession is made up of dominantly calciturbidites, carbonate breccias and conglomerates, along with mudstones that represent the pelagic/hemipelagic background sedimentation. It displays hectometric to outcrop-scale slump folds with variable hinge-line orientations and pinch-and-swell structures, evidencing soft-sediment deformation, consistent with a slope to base-of-slope setting. Three limestone samples from this succession include conodonts referable to the pandemic Hirsutodontus simplex Subzone of the Cordylodus intermedius Zone (upper Furongian, Cambrian) and from the Macerodus dianae Zone (upper Tremadocian, Ordovician), implying that a slope connected the shallow-water shelf with a deep-water (oceanic) basin at least since late Cambrian times. The conodont faunas show affinities to coeval assemblages from outer shelf and slope environments around Laurentia yet they are not conclusive to postulate a geographic origin for the Precordillera. The thermal alteration of the conodonts is consistent with sedimentary burial and nappe stacking in this sector of the Precordillera.