  We attempt to determine the nature of the high energy emission of the radio
galaxy 3C 111, by distinguishing between the effects of the thermal and
non-thermal processes. We study the X-ray spectrum of 3C 111 between 0.4 keV
and 200 keV, and its spectral energy distribution, using data from the Suzaku
satellite combined with INTEGRAL, Swift/BAT data, and Fermi/LAT data. We then
model the overall spectral energy distribution including radio and infrared
data. The combined Suzaku, Swift and INTEGRAL data are represented by an
absorbed exponentially cut-off power-law with reflection from neutral material
with a photon index Gamma = 1.68+-0.03, a high-energy cut-off Ecut = 227+143-67
keV, a reflection component with R = 0.7+-0.3 and a Gaussian component to
account for the iron emission-line at 6.4 keV with an equivalent width of EW =
85+-11 eV. The X-ray spectrum appears dominated by thermal, Seyfert-like
processes, but there are also indications of non-thermal processes. The radio
to gamma-ray spectral energy distribution can be fit with a single-zone
synchrotron-self Compton model, with no need for an additional thermal
component. We suggest a hybrid scenario to explain the broad-band emission,
including a thermal component (iron line, reflection) that dominates in the
X-ray regime and a non-thermal one to explain the spectral energy distribution.
