The simple Held and Hou (1980) nearly inviscid model of the axisymmetric atmospheric circulation, rationalizing the existence of Hadley cells, Jet Streams, and tropical homogenization of potential temperature and vorticity, is adapted to the oceanic subthermocline region. The meridional profile of radiative equilibrium temperature, which provides the driving in the atmospheric case, is replaced, in the oceanic case, by the large-scale equatorial doming of the thermocline. The meridional structure of the equatorial thermostad and the existence, at its poleward flanks, of eastward subsurface countercurrents coincident with sharp potential vorticity gradients are thus explained via angular momentum redistribution by secondary ageostrophic over-turning cells in the meridional plane. Taking into account the existence of the equatorial undercurrent within the thermocline has little effect on the overall structure of the subthermocline solution at a given longitude, even though homogenization of properties is less efficient.