  Blazars emit non-thermal radiation in all frequency bands from radio to
\gamma-rays. Additionally, they often exhibit rapid flaring events at all
frequencies with doubling time scale of the TeV and X-ray flux on the order of
minutes, and such rapid flaring events are hard to explain theoretically. We
explore the effect of the synchrotron-self Compton cooling, which is inherently
time-dependent, leading to a rapid cooling of the electrons. Having discussed
intensively the resulting effects of this cooling scenario on the spectral
energy distribution of blazars in previous papers, the effects of the
time-dependent approach on the synchrotron lightcurve are investigated here.
Taking into account the retardation due to the finite size of the source and
the source geometry, we show that the time-dependent synchrotron-self Compton
(SSC) cooling still has profound effects on the lightcurve compared to the
usual linear (synchrotron and external Compton) cooling terms. This is most
obvious if the SSC cooling takes longer than the light crossing time scale.
Then in most frequency bands the variability time scale is up to an order of
magnitude shorter than under linear cooling conditions. This is yet another
strong indication that the time-dependent approach should be taken into account
for modeling blazar flares from compact emission regions.
