  Unique data on $BVRI$ brightness curves of the OT of GRB 970508 obtained with
the 6-m telescope have been interpreted in the framework of the GRB-SN
(supernovae) connection. The effect must be maximal in the I_c band as OT GRB
970228. The peak absolute (M_B) magnitude of the suggested SN must be around
-19.5 for the OT of GRB 970508. If all or the main part of long GRBs are
associated with SNe, the GRB host galaxies (for ground-based observations, at
least) must be dimmer than the peak magnitude of the SN.
