  We present the results of photometric observations of the variable optical
source associated to the remnant of the gamma-ray burst GRB970508 performed at
SAO RAS (Russia) from May to August 1997. The observations were carried out
with the standard (Johnson-Kron-Cousins) photometric BVRcIc system using the
1-meter and 6-meter telescopes. The brightness of the optical source increased
from Rc=21.19 (May 9.75 UT) to Rc=19.70 (May 10.77 UT), whereupon it was
decaying in all the four BVRcIc bands during about one month after the burst.
Between the 3rd and the 6th night after the GRB970508 event, the flux decrease
of the optical source follows an exponential law in all the four bands. In that
period the broad-band spectrum of the object does not change and can be
approximately described by a power with index -1.1. The subsequent observations
showed a reduction of the source brightness decrease rate in all bands. The
source flux decay after the maximum in the Rc band is well described by a
single power-law with index -1.171 for the whole set of observations during 86
days. In the other bands the decay seems to slow down from the 31th day
onwards. In particular, in the Ic band the source magnitude is about 23.1 from
the 36th day after the GRB to the end of the observations (August 4, 1997).
