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).
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