After the positive detection by BeppoSAX of hard X-ray radiation up to simi
lar to 80 keV in the Coma Cluster spectrum, we present evidence for nonther
mal emission from A2256 in excess of thermal emission at a 4.6 sigma confid
ence level. In addition to this power-law component, a second nonthermal co
mponent already detected by ASCA could be present in the X-ray spectrum of
the cluster, which is not surprising given the complex radio morphology of
the cluster central region. The spectral index of the hard tail detected by
the Phoswich Detection System on board BeppoSAX is marginally consistent w
ith that expected for the inverse Compton model. A value of similar to 0.05
mu G is derived for the intracluster magnetic field of the extended radio
emission in the northern regions of the cluster, while a higher value of si
milar to 0.5 mu G could be present in the central radio halo, which is like
ly related to the hard tail detected by ASCA.