  We present a model of the spectra of gamma-ray emitting blazars in which a
single homogeneous emission region both emits synchrotron photons directly and
scatters them to high (gamma-ray) energy before emission (a ``synchrotron
self-Compton'' or SSC model). In contrast to previous work, we follow the full
time dependent evolution of the electron and photon spectra, assuming a
power-law form of the electron injection and examine the predictions of the
model with regard to variability of the source. We apply these computations to
the object Mkn 421, which displayed rapid variability in its X-ray and TeV
emission during a multiwavelength campaign in 1994. This observation strongly
implies that the same population of electrons produces the radiation in both
energy bands. By fitting first the observed quiescent spectrum over all 18
orders of magnitude in frequency, we show that the time dependence of the
keV/TeV flare could have been the result of a sudden increase in the maximum
energy of the injected electrons. We show also that different types of flare
may occur in this object and others, and that the energy band most sensitive to
the properties of the acceleration mechanism is the X-ray band.
