  We study bilayer quantum Hall systems at total Landau level filling factor
$\nu=1$ in the presence of interlayer tunneling and coupling to a dissipative
normal fluid. Describing the dynamics of the interlayer phase by an effective
quantum dissipative XY model, we show that there exists a critical dissipation
$\sigma_c$ set by the conductance of the normal fluid. For $\sigma > \sigma_c$,
interlayer tunnel splitting drives the system to a $\nu=1$ quantum Hall state.
For $\sigma <\sigma_c$, interlayer tunneling is irrelevant at low temperatures,
the system exhibits a superfluid transition to a collective quantum Hall state
supported by spontaneous interlayer phase coherence. The resulting phase
structure and the behavior of the in-plane and tunneling currents are studied
in connection to experiments.
