  Two coupled, interpenetrating fluids suffer instabilities beyond certain
critical counterflows. For ideal fluids, an energetic instability occurs at the
point where a sound mode inverts its direction due to the counterflow, while
dynamical instabilities only occur at larger relative velocities. Here we
discuss two relativistic fluids, one of which is dissipative. Using linearized
hydrodynamics, we show that in this case the energetic instability turns
dynamical, i.e., there is an exponentially growing mode, and this exponential
growth only occurs in the presence of dissipation. This result is general and
does not rely on an underlying microscopic theory. It can be applied to various
two-fluid systems for instance in the interior of neutron stars. We also point
out that under certain circumstances the two-fluid system exhibits a mode
analogous to the r-mode in neutron stars that can become unstable for
arbitrarily small values of the counterflow.
