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The local electric field has been derived analytically inside multilayer metallic films with weak nonlinearity, and hence the effective linear dielectric constant and third-order nonlinear susceptibility of the layered structures are calculated. As the number of layers increases, the comparison with the previous results of graded metallic films shows a gradual transition from sharp peaks to a broad continuous band. These results give further evidence of the emerging absorption band reported recently [J. P. Huang and K. W. Yu, Appl. Phys. Lett. 85, 94 (2004)]. Thus, multilayer metallic films can serve as optical materials with a giant enhancement of optical nonlinearity and a large figure of merit. [ABSTRACT FROM AUTHOR]