  We analyze spectrum of waveguide modes of an arbitrary uniaxial anisotropic
metamaterial slab with non-local electromagnetic response whose permittivity
tensor could be described within Drude approximation. Spatial dispersion was
introduced within the hydrodynamical model. Both anisotropy and spatial
dispersion were considered as perturbations. This helps to distinguish their
effect on the spectrum of the slab and to analyze lifting of the degeneracy of
eigenmodes at plasma frequency in detail. Spatial dispersion is shown to result
in break of the singularity in the den- sity of optical states in the
hyperbolic regime and in suppression of negative dispersion induced by
anisotropy. Mutual effect of spatial dispersion and anisotropy can bring light
to a complete stop at certain frequencies.
