  We determine the most general form of the equations of relativistic
superfluid hydrodynamics consistent with Lorentz invariance, time-reversal
invariance, the Onsager principle and the second law of thermodynamics at first
order in the derivative expansion. Once parity is violated, either because the
$U(1)$ symmetry is anomalous or as a consequence of a different parity-breaking
mechanism, our results deviate from the standard textbook analysis of
superfluids. Our general equations require the specification of twenty
parameters (such as the viscosity and conductivity). In the limit of small
relative superfluid velocities we find a seven parameter set of equations. In
the same limit, we have used the AdS/CFT correspondence to compute the parity
odd contributions to the superfluid equations of motion for a generic
holographic model and have verified that our results are consistent.
