An efficient frequency-dependent finite-element time-domain method for the analysis of dispersive media is presented. The formulation, based on the 2 nd-order wave equation, includes a slowly-varying envelope approximation (SVEA) and perfectly matched layers (PMLs), and the dispersion effects of the medium are incorporated by an accurate computation of the recursive evaluation of the convolution integral. Numerical examples in microwaves and optical frequencies are given to validate the proposed formulation. © 2004 Wiley Periodicals, Inc.