We demonstrate that fast moving hares in clusters of galaxies provide a pla
usible source of (extended) nonthermal Ii-ray and gamma -ray emission. This
follows from the fact that accelerated particles are produced in their bow
shocks. A substantial fraction of a virialized ensemble of halos can have
moderate supersonic velocities outside the central region of a rich cluster
. Dark matter halos of supersonic and superalfvenic velocity will create co
llisionless bow shocks of moderate Mach number M greater than or similar to
2 due to electromagnetic interaction between comoving baryonic matter and
the hot intra-cluster gas. We present kinetic modelling of nonthermal elect
ron injection, acceleration and propagation in such systems and conclude th
at the halos are efficient electron accelerators and sources of hard X-ray
and gamma -ray emission. Inverse-Compton radiation, bremsstrahlung, and syn
chrotron radiation by these electrons produce spectra that are in quantitat
ive agreement with e.g. the hard X-ray and radio emission observed from the
Coma cluster Moreover, the relative increase of hard X-ray emission outsid
e the central 0.3-0.4 Mpc of the cluster A2199, as observed by BeppoSAX, ca
n be understood in this framework. Spatially resolved hard X-ray and gamma
-ray spectra of clusters (e.g. INTEGRAL) can determine the contribution of
the energetic lepton component generated by supersonic halo motions to the
observed nonthermal emission, thus constraining the energetic nuclear compo
nent.