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An investigation of the propagation of electromagnetic pulses in a weakly nonlinear, cold, collisionless plasma is described. It is found that a transverse electromagnetic pulse generates, through nonlinear effects, a small amplitude, longitudinal electric pulse field. The transient behavior of this longitudinal electric field is studied. One particular case is considered in detail: the nonlinear generation of a longitudinal electric field by a transverse electromagnetic pulse which is excited by a suddenly turned-on cosinusoidal electric field of frequency . Computer plots of numerical calculations of the second-order transient longitudinal field are presented.