  The gamma-ray burst GB970508 was observed simultaneously by the Gamma Ray
Burst Monitor (GRBM) and one of the X-ray Wide Field Cameras (WFC) aboard
BeppoSAX. The latter provided a position within 1.9' radius. A series of
follow-up observations with the Narrow Field Intruments (NFI) was then
performed in a period from 6 hours to 6 days after the main event. A previously
unknown source, which we associate with the afterglow of the GRB, was
discovered in the error box. We find that, after the initial burst, X-ray
emission is still present and decays as t^(-1.1) up to 6 times 10^4 s. This is
followed by a burst of activity with a duration 10^5 s. The energy produced in
this event is a substantial fraction of the total energy of the GRB, which
means that the afterglow is not a remnant of the initial burst (the GRB) that
fades away smoothly. Our results support the idea that the processes generating
the GRB and its afterglow are the same.
