A general approach to analysis of Dyakonov surface waves at the interfaces of anisotropic biaxial crystals is proposed, taking into account arbitrary spatial orientation of the media tensors principal axes. This approach is based on the operator representation of macroscopic Maxwell equations corresponding to the quantum-mechanical equations for photon states in an inhomogeneous anisotropic media. Surface wave dispersion law is investigated in the most general case. It is established that the interface eigenmode dispersion is closely related to the dispersion of bulk waves in the partnering media, which is a specific feature of Dyakonov waves. The electromagnetic field spatial distribution is investigated in the direction orthogonal to the boundary plane. The surface wave angular existence domain is determined. It’s dependencies on the rotation angles of the media optical axes are studied as well.