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 media͒. 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 nonlocal constitutive relations have been usually considered in the past as a secondorder 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 metamaterials͒, the reported results open the question of the relevance of the spatial dispersion in the characterization of these artificial media. Causality imposes that all material media must be dispersive. In most cases this behavior results in local dispersive constitutive relations, i.e., in frequency-dependent constitutive permittivity and permeability tensors. Nonlocal dispersive behavior ͑i.e., spatial dispersion͒, which results in constitutive operators depending also on the spatial derivatives of the mean fields ͑or, for plane electromagnetic waves, on the wave-vector components͒, is usually considered as a small effect, meaningful in the short-wavelength limit. Specifically, spatial dispersion will always appear when the higher-order terms in the series expansion of the constitutive parameters in power series of the dimensionless parameter a/ (a is the lattice constant of the crystal and the wavelength inside the medium͒ are not neglected.