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Electromagnetic localization and the existence of gap solitons in nonlinear metamaterials, which exhibit a stop band in their linear spectral response, is theoretically investigated. For a self-focusing Kerr nonlinearity, the equation for the electric field envelope with carrier frequency in the stop band—where the magnetic permeability µ(?) is positive and the dielectric permittivity Ƹ(?) is negative—is described by a nonlinear Klein–Gordon equation with a dispersive nonlinear term. A family of standing and moving localized waves for both electric and magnetic fields is found, and the role played by the nonlinear dispersive term on solitary wave stability is discussed. [ABSTRACT FROM AUTHOR]