  It is shown that a Bose gas of two-level atoms in the intense resonant laser
field at zero temperature is a mixture of two condensates with a definite ratio
of the densities. The criteria of stability are found for the stationary states
of such system against the increment of the amplitudes of quasi Bogoliubov
elementary excitations. Besides the usual acoustic mode the gap mode is shown
to exist and the magnitude of the gap is proportional to the laser field
amplitude. The involvement of the gas nonideality under definite conditions
results in an instability and decay of the condensates.
