Correlated spectral and temporal variability in the high-energy emission from blazars

Blazar Bare data show energy-dependent lags and correlated variability betw een optical/X-ray and GeV-TeV energies, and follow characteristic trajector ies when plotted in the spectral-index/flux plane. This behavior is qualita tively explained if nonthermal electrons are injected over a finite time in terval in the comoving plasma frame and cool by radiative processes. Numeri cal results are presented which show the importance of the effects of synch rotron self-Compton cooling and plasmoid deceleration. The use of INTEGRAL to advance our understanding of these systems is discussed.