It is well known that for general evolution problems it is not necessarily possible to infer linear stability from spectra. Known counterexamples include hyperbolic PDEs. A possible way out of this is to investigate criteria in addition to the spectrum which would imply stability. Such criteria are typically based on a WKB type approximation for short wave disturbances. In recent work by Shvydkoy, such criteria, originally developed for the Euler equations, are generalized to a class of equations he calls ``advective.'' It is proved that creeping flows of nonlinear viscoelastic fluids of Maxwell type fall into this category. Shvydkoy's results are for problems with periodic boundary conditions. If homogeneous Dirichlet conditions are imposed on the boundary, it can be shown that wall modes are spectrally determined, and stability can still be decided on the basis of Shvydkoy's criterion. In addition to the spectrum of the linearized operator, this involves determining the stability of a variable coefficient ODE system along each streamline of the base flow. It is also proved that linear stability implies nonlinear stability for small perturbations.