  Correspondence between frequency and energy spectra and biorthogonality
conditions for the excitations of Bose-Einstein condensates described by
Gross-Pitaevskii model have been derived selfconsistently revealing several
novel aspects originating in nonselfadjoitness of the Bogoliubov operator. It
has been demonstrated that frequency resonances of the excitations with
positive and negative energies can lead to their mutual annihilation and
appearance of the collective modes with complex frequencies and zero energies.
Conditions for the avoided crossing of energy levels have also been discussed.
General theory has been verified both numerically and analytically in the weak
interaction limit considering an example of vortices in a binary mixture of
condensates. Growth of excitations with complex frequencies leads to spiraling
of the unit and double vortices out of the condensate center to its periphery
and to splitting of the double and higher order vortices to the unit ones.
