After the positive detection by BeppoSAX of hard X-ray radiation up to ~80 keV in the Coma cluster spectrum, we present evidence for nonthermal emission from A2256 in excess of thermal emission at a 4.6sigma confidence level. In addition to this power law component, a second nonthermal component already detected by ASCA could be present in the X-ray spectrum of the cluster, not surprisingly given the complex radio morphology of the cluster central region. The spectral index of the hard tail detected by the PDS onboard BeppoSAX is marginally consistent with that expected by the inverse Compton model. A value of ~0.05 microG is derived for the intracluster magnetic field of the extended radio emission in the northern regions of the cluster, while a higher value of ~0.5 microG could be present in the central radio halo, likely related to the hard tail detected by ASCA.