  We analyze the existence of localized waves in the vicinities of the
interface between two dielectrics, provided one of them is uniaxial and lossy.
We found two families of surface waves, one of them approaching the well-known
Dyakonov surface waves (DSWs). In addition, a new family of wave fields exists
which are tightly bound to the interface. Although its appearance is clearly
associated with the dissipative character of the anisotropic material, the
characteristic propagation length of such surface waves might surpasses the
working wavelength by nearly two orders of magnitude.
