Abstract. The Method of Lines (MoL) is a semi-analytical numerical algorithm that has been used in the past to solve Maxwell's equations for waveguide problems. It is mainly used in the frequency domain. In this paper it is shown how the MoL can be used to solve initial value problems in the time domain. The required expressions are derived for one-dimensional structures, where the materials may be dispersive. The algorithm is verified with numerical results for homogeneous structures, and for the concatenation of standard dielectric and left handed materials.