  At the filling factor $\nu$=2, the bilayer quantum Hall system has three
phases, the spin-ferromagnet phase, the spin singlet phase and the canted
antiferromagnet (CAF) phase, depending on the relative strength between the
Zeeman energy and interlayer tunneling energy. We present a systematic method
to derive the effective Hamiltonian for the Goldstone modes in these three
phases. We then investigate the dispersion relations and the coherence lengths
of the Goldstone modes. To explore a possible emergence of the interlayer phase
coherence, we analyze the dispersion relations in the zero tunneling energy
limit. We find one gapless mode with the linear dispersion relation in the CAF
phase.
