Collective elementary excitations of two-dimensional electron-hole system in a strong perpendicular magnetic field were considered in two different ground states: Bose-Einstein condensation (BEC) of magnetoexcitons and metallic-type electron-hole liquid (EHL). The BoseEinstein condensation (BEC) with arbitrary wave vector was investigated in Hartree-Fock-Bogoliubov approximation as well as beyond it taking into account the correlation energy. The breaking of the gauge symmetry of the Hamiltonian was introduced following the idea proposed by Bogoliubov in his theory of quasi-averages. The equations of motion were written in the frame of the starting electron and hole creation and annihilation operators. The chains of equations of motion for a set of Green's functions describing the exciton-type excitations as well as the plasmon-type excitations were deduced. The energy spectrum of the collective elementary excitations is characterized by the interconnection of the exciton and plasmon branches, because in 2D electron-hole liquid in a strong perpendicular magnetic field the plasmon-type elementary excitations are gapless and are lying in the same spectral interval as the exciton-type elementary excitations. The taking into account of the concentration contributions was made in two approximations, one of them in HFBA and another one beyond HFBA with the correlation corrections. The concentration terms gives rise to the proper dispersion law for the acoustical plasmon branch as well as add some terms to the excitonic branches. The excitonic branches are doubled because these contributions are added with different signs, what can be explained by the formation of exciton-plasmon complexes. The intra-Landau level excitations of the two-dimensional electron-hole liquid are characterized by two branches of the energy spectrum. 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 behavior at the intermediary values of the wave vectors and monotonically increases with saturation similar to the case of acoustical branch.