  A large-$N_{\rm c}$ expansion is combined with the Kubo formalism to study
the shear viscosity $\eta$ of strongly interacting matter in the two-flavor NJL
model. We discuss analytical and numerical approaches to $\eta$ and investigate
systematically its strong dependence on the spectral width and the
momentum-space cutoff. Thermal effects on the constituent quark mass from
spontaneous chiral symmetry breaking are included. The ratio $\eta/s$ and its
thermal dependence are derived for different parameterizations of the spectral
width and for an explicit one-loop calculation including mesonic modes within
the NJL model.
