  We theoretically investigate the existence and properties of hybrid surface
waves forming at interfaces between left-handed materials and dielectric
birefringent media. The existence conditions of such waves are found to be
highly relaxed in comparison to the original hybrid surface waves, discovered
by Dyakonov, in configurations involving birefringent materials and
right-handed media. Hybrid surface waves in left-handed materials feature
remarkable properties: (i) a high degree of localization and (ii) coexistence
of several guided solutions. The existence of several hybrid surface waves for
the same parameter set is linked to the birefringent nature of the medium
whereas the strong localization is related to the presence of the left-handed
material. The hybrid surface modes appear for large areas in the parameter
space.
