The intra-Landau-level excitations of the two-dimensional electron-hole liquid are characterized by two branches of the energy spectrum. The acoustical plasmon branch with in-phase oscillations of electrons and holes has a linear dispersion law in the range of small wavevectors, with a velocity which does not depend on the magnetic field strength, and monotonically increases with saturation at higher values of the wavevectors. The optical plasmon branch with oscillations of electrons and holes in opposite phases has a quadratic dependence in the range of long wavelength, a weak roton-type behaviour at the intermediary values of the wavevectors and monotonically increases with saturation similar to the case of the acoustical branch. The influence of the supplementary in-plane electric field leads to the drift of the charged particles in the crossed electric and magnetic fields and to the energy spectrum as in the reference frame, where the e-h system is moving with the drift velocity. A perturbation theory using the Green function method is developed on the basis of a small parameter v²(1-v²), where v ² is the filling factor and (1-v²) displays the phase space filling effect. © 2009 IOP Publishing Ltd.