We here study the scouring processes that evolve around a submarine pipeline placed on a weakly cohesive seabed. We first analyze some laboratory tests carried out by Vijaya Kumar et al. [21], Xu et al. [25] and Zhou et al. [28] that focused on the scouring around a horizontal cylinder lying on a cohesive bed, subject to waves and currents. The specific purpose is that of finding a new formula for the prediction of the equilibrium scour depth under submarine pipelines. After a theoretical analysis of the main parameters, the sought formula has been found to be a function of: (i) the hydrodynamic forces acting on the cylinder (through the Keulegan-Carpenter parameter KC), (ii) the clay content of the soil C-c, and (iii) the burial depth eo ID. In the presence of small amounts of clay (C-c< 5%), the scour depth depends directly on KC (as confirmed by many literature works for pipelines lying on sandy soils, e.g.[18]) and inversely on C-c (as already seen for bridge abutments on cohesive soils, e.g. [1]), the best-fit law being characterized by a coefficient of determination R-2 = 0.62. If some burial depth is accounted for, this being a novelty of the present work, a more general formulation can be used, valid in the presence of weakly-cohesive soils and with burial depths of the pipe smaller than 0.5 (R-2 = 0.79). For large clay-content ranges (2%