An algorithm accounting for dispersive and third-order nonlinear effects in a vector two-dimensional FDTD method is developed and validated in this paper. Kerr and Raman phenomena are implemented in FDTD using a new approach, which combines the accuracy of a rigorous FDTD update scheme and the speed of an approximate solution. As it is shown in this paper, the proposed method is applicable to the mode analysis of waveguide structures, like photonic crystal fibers, where the appropriate balance between dispersion and nonlinear phenomena is essential for supercontinuum generation. Several computational examples discussed in this paper successfully validate the proposed method.