This chapterFrequency-dependent FDTD method presents the details of the frequency-dependent formulations for the analysis of plasmonic devices consisting of dispersive media. Three frequently-used techniques are given such as the auxiliary differential equation (ADE), recursive convolution (RC)-related and Z-transform (ZT) techniques. The ADE technique is based on the use of differential equation explaining the relation between D and E. The D-E equation in time domain is discretized by the finite-difference scheme and simultaneously solved with the original FDTD equations. In the RC-related techniques, the convolution calculation between the permittivity and the electric field can be efficiently treated with a recursive procedure. The original RC technique is first-order accurate with one convolution calculation, while the piecewise linear RC (PLRC)Piecewise Linear RC (PLRC)  technique is second-order accurate with two convolution calculations. The trapezoidal RC (TRC)Trapezoidal RC (TRC) technique technique is second-order accurate even with one convolution calculation. In the ZT technique, the complicated convolution integrals can simply be reduced to algebraic equations, and the D-E relation can be transformed into finite-difference equations. Here, these three techniques are explained for the Drude and Drude-Lorentz models. In addition, the Drude-Critical points (D-CP) model is also investigated with the TRC technique. The application to the implicit LOD-FDTD method is also discussed and the accuracy of the frequency-dependent formulations is compared.