The transition line matrix (TLM) method, since it is a time-domain met
hod, cannot deal directly with dispersive media. We propose a way for
modeling such media, starting from the causality relationship between
field vectors D and E, which is discretized over the same space-time m
esh as the two-dimensional TLM mesh, This leads to adding a voltage so
urce at each node, its value depending on the previous instants, The m
ethod is validated by computing the reflection coefficient at an air-w
ater interface and the cutoff frequencies of a rectangular waveguide c
ontaining a Debye dielectric.