  We monitored the BL Lac object S5 0716+714 in the optical band during the
period November 1994-April 1995, which includes the time of a gamma-ray
observation by the Energetic Gamma Ray Experiment Telescope (EGRET) on February
14--28, 1995. The light curves in the R and B bands show fast fluctuations
superimposed on longer timescale variations. The color index correlates with
intensity during the rapid flares (the spectrum is flatter when the flux is
higher), but it is rather insensitive to the long term trends. Over the 5 month
observational period the light curve shows an overall brightening of about 1
mag followed by a fast decline. The EGRET pointing covers part of the very
bright phase (V about 13.2) and the initial decline. An ultraviolet spectrum
was also obtained with the International Ultraviolet Explorer (IUE) (1200-3000
A) during the EGRET observations. The variability of the optical emission of S5
0716+714 by itself sets important constraints on the magnetic field strength
and on the physical processes responsible for it. Interpreting the whole
electromagnetic spectrum with synchrotron self Compton models leads to the
prediction of a bright gamma-ray state during the EGRET pointing. We discuss
how the gamma-ray data could be used as a diagnostic of the proposed models.
