Starting from the equations of hydrodynamics, which include both collisional and collisionless ideal fluids, the main properties of pseudo-barotropes are revisited and special attention is deserved to a necessary condition for equilibrium, i.e. the coincidence of the boundary with an isopotential (gravitational + centrifugal) surface. By use of the above condition, a new method is formulated to find bifurcation points from axisymmetric to triaxial pseudo-barotropic sequences.