The offshore Campos Basin, located in Southeastern Brazil represents an important area in the Brazilian economy as it is one of the most prolific oil-producing basins in the country. With the development of offshore infrastructures in this region, structural design and location must consider different geohazards. This paper addresses the seismic response of gentle submarine slopes subjected to small-to-moderate-sized earthquakes, representative of the Brazilian seismic conditions. The seismic analyses employed numerical modeling, with a nonlinear constitutive model.A set of bedrock ground motions representative of the offshore Campos Basin seismicity was obtained, employing a Uniform Hazard Response spectrum for the region and earthquakes from the Pacific Earthquake Engineering Research (PEER) database. Numerical modelling results showed that, even for small slope angles and moderate earthquakes, there is an accumulation of permanent displacements and shear strains in the downslope direction can affect the stability and performance of existing offshore infrastructures. The findings of this research provide a valuable reference for the prediction of seismic displacements, shear strains and seabed amplification or attenuation of earthquakes on gentle slopes in deep-water deposits similar to those found in the offshore Campos Basin.