  It is found that there exist composite media that exhibit strong spatial
dispersion even in the very large wavelength limit. This follows from the study
of lattices of ideally conducting parallel thin wires (wire media). In fact,
our analysis reveals that the description of this medium by means of a local
dispersive uniaxial dielectric tensor is not complete, leading to unphysical
results for the propagation of electromagnetic waves at any frequencies. Since
non--local constitutive relations have been usually considered in the past as a
second order approximation, meaningful in the short wavelength limit, the
aforementioned result presents a relevant theoretical interest. In addition,
since such wire media have been recently used as a constituent of some discrete
artificial media (or metamaterials), the reported results open the question of
the relevance of the spatial dispersion in the characterization of these
artificial media.
