We report on the results of optical follow-up observations of the counterpart of GRB 970508 , starting 7 hours after the event .
Multi-color U , B , V , R _ { c } and I _ { c } band observations were obtained during the first three consecutive nights .
The counterpart was monitored regularly in R _ { c } until \sim 4 months after the burst .
The light curve after the maximum follows a decline that can be fitted with a power law with exponent \alpha = –1.141 \pm 0.014 .
Deviations from a smooth power law decay are moderate ( r.m.s .
= 0.15 magnitude ) .
We find no flattening of the light curve at late times .
The optical afterglow fluence is a significant fraction , \sim 5 % , of the GRB fluence .
The optical energy distribution can be well represented by a power law , the slope of which changed at the time of the maximum ( the spectrum became redder ) .