In this paper, we study theoretical formalism of the surface magnetostatic modes of a left-handed cylindrical shell (i.e. a cylindrical shell with both negative dielectric permittivity and negative magnetic permeability) with a dielectric core and provide an explicit form of the dispersion relation for surface magnetostatic modes, in terms of interaction between the bare modes of the individual surfaces of the cylindrical shell. In the case of a metallic core, we found only one magnetostatic mode for each angular momentum.
