  Motivated by recent reports of strongly correlated radio and X-ray
variability in 3C279 (Grandi, etal 1995), we have computed the relative
amplitudes of variations in the synchrotron flux at $\nu$ and the self-Compton
X-ray flux at 1 keV ($R(\nu)$) for a homogeneous sphere of relativistic
electrons orbiting in a tangled magnetic field. Relative to synchrotron
self-Compton scattering without induced Compton scattering, stimulated
scattering reduces the amplitude of $R(\nu)$ by as much as an order of
magnitude when $\tau_T \gtwid 1$. When $\tau_T$ varies in a fixed magnetic
field, $R_{\tau}$ increases monotonically from 0.01 at $\nu_o$, the
self-absorption turnover frequency, to $0.5$ at $100 \nu_o$. The relative
amplitudes of the correlated fluctuations in the radio-mm and X-ray fluxes from
3C279 are consistent with the synchrotron self-Compton model if $\tau_T$ varies
in a fixed magnetic field and induced Compton scattering is the dominant source
of radio opacity. The variation amplitudes are are too small to be produced by
the passage of a shock through the synchrotron emission region unless the
magnetic field is perpendicular to the shock front.
