In this paper we review and discuss the possibility of having a 2D-nematic ordering of the surfactant polar heads in bilayer membranes. The coupling between the nematic order parameters and the curvature can yield instabilities in the shape of the membrane, generally leading to tubules with mesoscopic radiuses. The nematic directors in the two monolayers should present coupled disclinations with peculiar characteristics. Para-nematic membranes, i.e., nematic membranes that are in the isotropic phase when flat, should behave as the nematic membranes in the curved state.