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We analyze spectrum of waveguide modes of an arbitrary uniaxial anisotropicmetamaterial slab with non-local electromagnetic response whose permittivitytensor could be described within Drude approximation. Spatial dispersion wasintroduced within the hydrodynamical model. Both anisotropy and spatialdispersion were considered as perturbations. This helps to distinguish theireffect on the spectrum of the slab and to analyze lifting of the degeneracy ofeigenmodes at plasma frequency in detail. Spatial dispersion is shown to resultin break of the singularity in the den- sity of optical states in thehyperbolic regime and in suppression of negative dispersion induced byanisotropy. Mutual effect of spatial dispersion and anisotropy can bring lightto a complete stop at certain frequencies.

Interplay between anisotropy and spatial dispersion in metamaterial waveguide