Rapidly rotating stars may be subject to a secular instability driven by viscosity. The oscillation modes that are susceptible to this instability are studied here in models of rigidly rotating neutron stars based on the polytropic and on several more realistic equations of state. For the polytropic models we confirm the classical result: that sufficiently rapidly rotating stars with adiabatic index γ > 2.237 suffer from the viscous instability, while those with γ < 2.237 do not. For the more realistic models we find no viscous instability in the 1.4 solar mass models from any equation of state. In sufficiently massive and rapidly rotating models, however, we do find the viscous instability in stars constructed from some of the realistic equations of state.
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