  We present an effective Hamiltonian for a bilayer quantum Hall system at
filling factor $\nu=1$ neglecting charge fluctuations. Our model is formulated
in terms of spin and pseudospin operators and is an exact representation of the
system within the above approximation. We analyze its low-lying excitations in
terms of spin-wave theory. Moreover we add to previous first-principle
exact-diagonalization studies concentrating on the quantum phase transition
seen in this system.
