Using the Nordic Optical Telescope, La Palma, Spain, optical studies of OT/GRB970508 were initiated 3 hours 5 minutes after the high energy event (This appears to be sooner than achieved elsewhere, for any optical transient). The OT was clearly detected in the earliest images. The last observation was done August 13-15, i.e. 95-97 days after the event. We have combined the NOT R and unfiltered data with similar photometry from elsewhere. We conclude that the observed source brightness cannot easily be modeled by theories predicting a monotonic rise to maximum. Also the post-maximum power-law decay, albeit predicted by several models, is no longer valid at the moment of our last observation. The contribution of a constant source, mR=25.5 is indicated, but this does not show up in the image profile.