  We present the results of a series of optical, UV, X-ray and gamma-ray
observations of the BL Lac object S50716+714 carried out by the Swift and AGILE
satellites in late 2007 when this blazar was flaring close to its historical
maximum at optical frequencies. We have found that the optical through soft
X-ray emission, likely due to Synchrotron radiation, was highly variable and
displayed a different behavior in the optical UV and soft X-ray bands. The 4-10
keV flux, most probably dominated by the inverse Compton component, remained
instead constant. The counting statistics in the relatively short AGILE GRID
observation was low and consistent with a constant gamma-ray flux at a level
similar to the maximum observed by EGRET. An estimate of the gamma-ray spectral
slope gives a value of the photon index that is close to 2 suggesting that the
peak of the inverse Compton component in the Spectral Energy Distribution (SED)
is within the AGILE energy band. The different variability behavior observed in
different parts of the SED exclude interpretations predicting highly correlated
flux variability like changes of the beaming factor or of the magnetic field in
simple SSC scenarios. The observed SED changes may instead be interpreted as
due to the sum of two SSC components, one of which is constant while the other
is variable and with a systematically higher synchrotron peak energy.
