We present the results of photometric observations of the variable opt
ical source associated to the remnant of the gamma-ray burst GRB 97050
8 performed at the Special Astrophysical Observatory of the Russian Ac
ademy of Science (SAO RAS) from May to August 1997. The observations w
ere carried out with the standard (Johnson-Kron-Cousins) photometric B
VRcTc system using the 1-meter and 6-meter telescopes. The brightness
of the optical source increased from R-c = 21.19 +/- 0.25 (May 9.75 UT
) to R-c = 19.10 +/- 0.03 (May 10.77 UT), whereupon it was decaying in
all the four BVRcIc bands during about one month after the burst. Bet
ween the 3rd and the 6th night after the GRB 970508 event, the flux de
crease of the optical source follows an exponential law in all the fou
r bands. In that period the broad-band spectrum of the object does not
change and can be approximately described by the power law F-nu propo
rtional to nu(-1.1). The subsequent observations in BVRcTc bands have
shown a reduction of the source brightness decrease rate. The source f
lux decay after the maximum in the R-c band is well described by a sin
gle power-law F proportional to t(-1.171(+/-0.012)) 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 I-c band th
e source magnitude is about 23.1 from the 36th day after the GRB to th
e end of the observations (August 4, 1997).