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 flare 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 ( Mattox et al . 1996 ) . Approximate agreement of theoretical and observed light curves is obtained for a viewing angle \theta _ { obs } \sim 0.1 rad , a black hole mass M \sim 3 \times 10 ^ { 9 } M _ { \odot } , and a magnetic field at the base of the jet B _ { o } \sim 10 ^ { 3 } G .