We present a new Suzaku observation of the obscured AGN in NGC 1365, revealing an unexpected excess of X-rays above 20 keV of at least a factor ~2 with respect to the extrapolation of the best-fitting 3-10 keV model. Additional Swift-BAT and Integral
-IBIS observations show that the 20-100 keV is concentrated within ~1.5 arcmin from the center of the galaxy, and is not significantly variable on time scales from days to years. A comparison of this component with the 3-10 keV emission, which is characterized by a rapidly variable absorption, suggests a complex structure of the circumnuclear medium, consisting of at least two distinct components with rather different physical properties, one of which covering >80% of the source with a column density NH~3-4x10^24 cm^(-2). An alternative explanation is the presence of a double active nucleus in the center of NGC 1365.
