A model is developed for the time dependent electromagnetic-radio to gamma-ray-emission of active galactic nuclei, specifically, the blazars, based on the acceleration and creation of leptons at a propagating discontinuity or front of a self-collimated Poynting flux jet. The front corresponds to a discrete relativistic jet component as observed with very long baseline interferometry (VLBI). Equations are derived for the number, momentum, and energy of particles in the front taking into account synchrotron, synchrotron-self-Compton (SSC), and inverse-Compton processes as well as photon-photon pair production. The apparent synchrotron, SSC, and inverse Compton luminosities as functions of time are determined. Predictions of the model are compared with observations in the gamma, optical, and radio bands. The delay between the high-energy gamma-ray hare and the onset of the radio is explained by self-absorption and/or free-free absorption by external plasma. Two types of gamma-ray flares are predicted: Compton dominated or SSC dominated, depending on the initial parameters in the front. The theory is applied to the recently observed gamma-ray flare of the blazar PKS 1622-297 (Matter et al. 1997). Approximate agreement of theoretical and observed light curves is obtained for a viewing angle theta(obs) similar to 0.1 rad, a black hole mass M similar to 3 x 10(9) M., and a magnetic field at the base of the jet B-0 similar to 10(3) G.