  The origin of the nonthermal EUV and hard X-ray emission "excess" reported
from some galaxy clusters has been intensively debated over last several years.
The most favored models which refer this excess to relativistic electrons
upscattering the 2.7 K CMBR generally requires very low magnetic field,
significantly below the estimates derived from the Faraday Rotation
Measurements, unless one invokes rather nonstandard assumptions concerning the
energy and pitch angle distributions of nonthermal electrons. In this paper we
suggest a new model assuming that the "nonthermal" excess is due to synchrotron
radiation of ultrarelativistic (multi-TeV) electrons of "photonic" origin.
These electrons are continuously introduced throughout the entire intracluster
medium by very high energy (hypothetical) gamma-rays through interactions with
the diffuse extragalactic radiation fields. We present numerical calculations
for the Coma cluster, and briefly discuss implications of the model for other
galaxy clusters both in the X- and gamma-ray energy domains.
