  The interaction of the nonlinear internal waves with a nonuniform current
with a specific form, characteristic for the equatorial undercurrent, is
studied. The current has no vorticity in the layer, where the internal wave
motion takes place. We show that the nonzero vorticity that might be occuring
in other layers of the current does not affect the wave motion. The equations
of motion are formulated as a Hamiltonian system.
