A time-domain study of the propagation of a light pulse is made by the finite-difference time-domain method. This method is described briefly and then two applications are presented: creation and diffraction of surface plasmons in the time-domain, and propagation of a light pulse through two tip models, a dielectric one and a metal-coated one. Results on propagation speed of surface plasmons, spatio-temporal shape and spectral study of the field emitted by a tip are presented.