  The nature of the broad-band spectra of supermassive accreting black holes in
active galactic nuclei (AGNs) is still unknown. The hard X-ray spectra of
Seyferts as well as of Galactic stellar-mass black holes (GBHs) are well
represented by thermal Comptonization, but the origin of the seed photons is
less certain. The MeV tails observed in GBHs provide evidence in favour of
non-thermal electron tails and it is possible that such electrons are also
present in the X-ray emitting regions of AGNs. Using simulations with the
kinetic code that self-consistently models electron and photon distributions,
we find that the power-law-like X-ray spectra in AGNs can be explained in terms
of the synchrotron self-Compton radiation of hybrid thermal/non-thermal
electrons, similarly to the hard/low state of GBHs. Under a very broad range of
parameters the model predicts a rather narrow distribution of photon spectral
slopes consistent with that observed from LINERs and Seyferts at luminosities
less than 3 per cent of the Eddington luminosity. The entire infrared to X-ray
spectrum of these objects can be described in terms of our model, suggesting a
tight correlation between the two energy bands. We show that the recently found
correlation between slope and the Eddington ratio at higher luminosities can be
described by the increasing fraction of disc photons in the emitting region,
which may be associated with the decreasing inner radius of the optically thick
accretion disc. The increasing flux of soft photons is also responsible for the
transformation of the electron distribution from nearly thermal to almost
completely non-thermal. The softer X-ray spectra observed in narrow-line
Seyfert galaxies may correspond to non-thermal Comptonization of the disc
photons, predicting that no cutoff should be observed up to MeV energies in
these sources, similarly to the soft-state GBHs.
