  We study two-fluid systems with nonzero fluid velocities and compute their
sound modes, which indicate various instabilities. For the case of two
zero-temperature superfluids we employ a microscopic field-theoretical model of
two coupled bosonic fields, including an entrainment coupling and a
non-entrainment coupling. We analyse the onset of the various instabilities
systematically and point out that the dynamical two-stream instability can only
occur beyond Landau's critical velocity, i.e., in an already energetically
unstable regime. A qualitative difference is found for the case of two normal
fluids, where certain transverse modes suffer a two-stream instability in an
energetically stable regime if there is entrainment between the fluids. Since
we work in a fully relativistic setup, our results are very general and of
potential relevance for (super)fluids in neutron stars and, in the
non-relativistic limit of our results, in the laboratory.
