  The time dependent synchrotron emission from relativistic jets, and the
relation between the synchrotron and ERC emission is considered within the
framework of the radiative front model. The timescale and profile of the
optically thin emission are shown to be determined, in this model, by the shock
formation radius, the thickness of expelled fluid slab and the variation of the
front's parameters due to its transverse expansion. For a range of reasonable
conditions, a variety of flare shapes can be produced, varying from roughly
symmetric with exponential rises and decays, as often seen in blazars, to
highly asymmetric with a fast rise and a much slower, power law decay, as seen
in GRB afterglows. The onset, duration, and fluence of low-frequency (below the
initial turnover frequency) and hard gamma-ray (above the initial gamma-spheric
energy) outbursts are limited by opacity effects; the emission at these
energies is quite generally delayed and, in the case of sufficiently short
length outbursts, severely attenuated. The observational consequences are
discussed. One distinctive prediction of this model is that in a single,
powerful source, the upper cutoff of the gamma-ray spectrum should be
correlated with the timescale of the outburst and with the amplitude of
variations at long wavelengths (typically radio to millimeter).
