  The collective elementary excitations of two dimensional magnetoexcitons in a
Bose Einstein condensate with zero wavevector are investigated in the framework
of the Bogoliubov theory of quasi averages. The Hamiltonian of the electrons
and holes lying in the lowest Landau levels contains supplementary interactions
due to virtual quantum transitions of the particles to the excited Landau
levels and back. As a result, the interaction between the magnetoexcitons zero
wavenumbers does not vanish and their BEC becomes stable. The energy spectrum
contains only one gapless,true Nambu Goldstone mode of the second kind,
proportional to the square of wavenumber at small values of wavenumber
describing the optical plasmon type oscillations. There are two exciton type
branches corresponding to normal and abnormal Green functions. Both modes are
gapped with roton type segments at intermediary values of the wavevectors and
can be named quasi NG modes. The fourth branch is the acoustical plasmon type
mode with absolute instability in the region of small and intermediary values
of the wavevectors. All branches have a saturation type dependencies at great
values of the wave vectors. The number and the kind of the true NG modes are in
accordance with the number of the broken symmetry operators.
