  Evidence for non-thermal activity in clusters of galaxies is well established
from radio observations of synchrotron emission by relativistic electrons. New
windows in the Extreme Ultraviolet and Hard X-ray ranges have provided for more
powerful tools for the investigation of this phenomenon. Detection of hard
X-rays in the 20 to 100 keV range have been reported from several clusters of
galaxies, notably from Coma and others. Based on these earlier observations we
identified the relatively high redshift cluster 1E0657-56 (also known as RX
J0658-5557) as a good candidate for hard X-ray observations. This cluster, also
known as the bullet cluster, has many other interesting and unusual features,
most notably that it is undergoing a merger, clearly visible in the X-ray
images. Here we present results from a successful RXTE observations of this
cluster. We summarize past observations and their theoretical interpretation
which guided us in the selection process. We describe the new observations and
present the constraints we can set on the flux and spectrum of the hard X-rays.
Finally we discuss the constraints one can set on the characteristics of
accelerated electrons which produce the hard X-rays and the radio radiation.
