  Observations of blazar flaring states reveal remarkably different variability
time scales. Especially rapid flares with flux doubling time scales of the
order of minutes have been puzzling for quite some time. Many modeling attempts
use the well known linear relations for the cooling and emission processes in
the jet in a steady-state scenario, albeit the obvious strongly time-dependent
nature of flares. Due to the feedback of self-produced radiation with
additional scattering by relativistic electrons, the synchrotron-self Compton
(SSC) effect is inherently time-dependent. Although this feedback is usually
implemented in numerical treatments, only recently an analytical analysis of
the effects of this nonlinear behaviour has been performed. Here, we report our
results concerning the effect of the time-dependent SSC on the spectral energy
distribution (SED) of blazars. We calculated analytically the synchrotron and
the SSC component, giving remarkably different spectral features compared to
the standard linear approach. Adding an external photon field to the original
setting, we could implement quite easily the effect of an additional external
Compton (EC) cooling, since such strong external photon fields are observed in
flat spectrum radio quasars (FSRQ), a subclass of blazars. Calculating the
resulting flux due to the EC cooling, we were able to show that the resulting
inverse Compton component strongly depends on the free parameters, and that SSC
could potentially have a strong effect in FSRQs, contrary to what is usually
assumed.
