  We discuss short wavelength (inertial wave) instabilities present in the
standard two-fluid neutron star model when there is sufficient relative flow
along the superfluid neutron vortex array. We demonstrate that these
instabilities may be triggered in precessing neutron stars, since the angular
velocity vectors of the neutron and proton fluids are misaligned during
precession. The presence of such an instability would render the standard,
solid body rotation, model for free precession inconsistent. Our results
suggest that the standard (Eulerian) slow precession that results for weak drag
between the vortices and the charged fluid (protons and electrons) is not
seriously constrained by the existence of the instability. In contrast, the
fast precession, which results when vortices are strongly coupled to the
charged component, is generally unstable. This implies that fast precession may
not be realised in astrophysical systems
