The graded sandstones in the Prealpine flysch basins of late Cretaceous to middle Eocene age in Switzerland range in modal composition from arkoses to litharenites. The detritus is characterized by rock fragments from the crystalline basement and sedimentary cover (with volcanics), together with glauconite and shallow-water fossil fragments. Some of the flysch basins can be differentiated by the proportions of various rock fragments. The model for internal divisions in graded sandstones (Bouma, 1962) is modified to include small current ripples in the lower and upper divisions of horizontal lamination. The sandstone sole markings in the Basal Schlieren and Waggital sequences are parallel to within-bed currents measured in the lower division of horizontal lamination, current ripple division, and upper division of horizontal lamination. Within-bed current directions were measured using charcoal and parting-step lineations, small and large current ripples, and convolute lamination. There was no measurable effect due to the Coriolis force as the currents slowed down and deposited individual graded beds. Sandstone paleocurrents flowed soutwestward in the Basal Schlieren flysch and southward in the Waggital flysch. Ocean-bottom currents that oriented charcoal particles in interbedded green shales and micrite limestone flowed parallel, in each basin, to the currents from which the graded sandstones were deposited. Under an hypothesis of deposition of the graded sandstones from turbidity currents, the parallelism of ocean-bottom currents with sandstone sole markings could be fortuitous. However, one would expect that any postulated, down-slope, gravity-controlled turbidity currents would commonly flow in a direction different than ocean-bottom currents. Consequently an hypothesis that the graded sandstones were deposited from waning ocean-bottom currents is a distinct possibility. Furthermore, scatter diagrams among the textural variables of mean size, standard deviation, and skewness for the graded sandstones and siltstones are similar to scatter diagrams for sandstones and siltstones deposited by normal bottom currents in numerous continental and marine environments.