We report on the results of optical follow-up observations of the counterpart of GRB970508 between 7 hours and 100 days after the event. Multi-colour U, B, V, Rc and Ic band observations were obtained during the first three consecutive nights. The Rc light curve rises to a maximum 1.8 days after the burst and after this declines with a power law decay, the exponent of which is α=-1.21+/-0.01. Superposed on this power law decay, we detect small amplitude (<0.5 magnitude) variations on timescales as short as half a day. The optical energy distribution can be well represented by a power law, the slope of which became steeper during the rise to maximum light and stayed constant afterwards.