The North Brazilian Coastal Current (NBCC) is idealized as an inertial, surface layer jet of equatorial origin, intruding along the coast into a northern water mass of constant, positive potential vorticity. Dissipation is accounted for by supposing that some equatorial water leaks out in the northwest corner of the intrusion. The problem is closed by adopting the free streamline boundary condition (between the northern and equatorial water masses) of continuous layer depth and velocity.Calculations are made for flow (intruding and return) supposed parallel to the coast; this approximation is verified à posteriori. The results show a narrow intrusion region along the coast, equatorial fluid flowing northwestward next to the coast, peeling off and returning along the boundary streamline. When no leakage is postulated, the northern limit of the intrusion becomes a stagnation point where the coast and the boundary streamline meet. With substantial leakage postulated, the flow chokes at some limiting latitude, where the inviscid inertial model breaks down. However, a realistic intrusion-return flow pattern is calculated south of the choking latitude for a number of different illustrative cases. The key control parameter is the potential vorticity of the northern water mass, or in a nondimensional form, the ratio of the rest-depths, at a given latitude, of the equatorial and northern water masses.The model accounts for a number of observed facets of NBCC behavior, notably its seasonal cycle, magnitude of the transports, intrusive and return flow.