  The spectrum of guided modes of linear chain of dielectric and left-handed
cylinders is analyzed. The structure of eigenfrequences is much more richer if
cylinders are made from the left-handed material with both permittivity and
permeability negative. he number of guided modes is much larger, and their
interaction with incident electromagnetic wave is much stronger. For some value
of the wave vector, no guided modes were found. We discuss how these specific
properties of guided modes correspond to folded bands, observed recently in
photonic structureswith left-handed components.
