  Recent observations of excess radiation at extreme ultraviolet and hard X-ray
energies straddling the well known thermal soft X-ray emission have provided
new tools and puzzles for investigation of the acceleration of nonthermal
particles in the intercluster medium of clusters of galaxies. It is shown that
these radiations can be produced by the inverse Compton upscattering of the
cosmic microwave background photons by the same population of relativistic
electrons that produce the well known diffuse radio radiation via the
synchrotron mechanism. It is shown that the commonly discussed discrepancy
between the value of the magnetic field required for the production of these
radiation with that obtained from Faraday rotation measures could be resolved
by more realistic models and by considerations of observational selection
effects. In a brief discussion of the acceleration process it is argued that
the most likely scenario is reacceleration of injected relativistic electrons
involving shocks and turbulence. The seed electrons cannot be the background
thermal electrons because of energetic considerations, and a steady state
situation may not agree with the details of the observed spectra. Episodic
generation of shocks and turbulence or episodic injection of relativistic
electrons is a more likely scenario for acceleration.
