  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 {\it front} of a 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 depending on pair creation
in the front.
