  Excitation spectra in bilayer quantum Hall systems at total Landau-level
filling $\nu=2$ are studied by the Hartree-Fock-Bogoliubov approximation. The
systems have the spin degrees of freedom in addition to the layer degrees of
freedom described in terms of pseudospin. On the excitation spectra from
spin-unpolarized and pseudospin-polarized ground state, this approximation
fully preserves the spin rotational symmetry and thus can give not only
spin-triplet but also spin-singlet excitations systematically. It is also found
that the ground-state properties are well described by this approximation.
