  An analytical theory of low frequency electromagnetic waves in metallic
photonic crystals with a small volume fraction of a metal is presented. The
evidence of the existence of such waves has been found recently via experiments
and computations. We have obtained an exact dispersion equation for omega (k)
and studied the cutoff frequency omega_0 = omega(0) as a function of parameters
of the photonic crystal. An analytical expression for the permittivity epsilon
is calculated. It is shown, that if the crystal is embedded into a medium with
negative mu, it has no propagating modes at any frequency. Thus, such a
compound system is not a left-handed material (LHM). The recent experimental
results on the LHM are discussed.

Condensed Matter