We report on the 0.5-200 keV spectral properties of Cyg X-1 observed at different epochs with the Narrow Field Instruments of the BeppoSAX satellite. The source was in its soft state during the first observation of 1996 June. In the second observation of 1996 September, the source had parameters characteristic to its hard state. A soft X-ray excess, a broad Fe Kα line and Compton reflection are clearly detected in both states. The soft-state broadband continuum is well modeled by a disk blackbody (accounting for the soft excess) and Compton upscattering of the disk photons by a hybrid, thermal/nonthermal plasma, probably forming a corona above the disk (also giving rise to the Compton-reflection component). In the hard state, the primary hard X-ray spectrum can be well modeled by Compton upscattering of a weak blackbody emission by a thermal plasma at a temperature of ~60 keV. The soft excess is then explained by thermal Comptonization of the same blackbody emission by another hot plasma cloud characterized by a low value of its Compton parameter. Finally, we find the characteristic ratio of the bolometric flux in the soft state to that in the hard state to be about 3. This value is much more compatible with theories of state transitions than the previously reported (and likely underestimated) value of 1.5.