A simple Sverdrup-type two-layer model that allows the outcropping of isopycnals is forced by wind stress, is completed with a frictional western boundary layer, and is investigated along the zero wind-stress curl line separating the subpolar gyre from the subtropical gyre. The study focuses on the different cross-gyre flow patterns. Intermediate length-scale dynamics, which is able to take the dispersion of Rossby waves and the steepening of isopycnals into account, is used to analyze the evolution of these cross-gyre currents. In particular, these transients show that the solution, which exhibits an arrested Rossby wave, is unstable in the western part of the basin. Nevertheless, this solution is able to evolve to other more stable solutions present in the dynamics: one in which there is an exchange of water masses between gyres and another one in which both gyres are independent. The first one has a deep (upper) slow northward (southward) flow in midoceanic regions and a strong western deep (upper) southward (northward) boundary current. This current system could well help to account for some of the transport in the western boundary undercurrent observed in the North Atlantic Ocean, and therefore the theory presented could indicate that the undercurrent and cross-gyre flow might have wind-driven components. The second stable solution, in which exchange is not allowed, would be rather representative of the North Pacific Ocean.