We have made BeppoSAX observations of the Seyfert 2/1.9 galaxy ESO103-G35, which contains a nuclear maser source and is known to be heavily absorbed in the X-rays. Analysis of the X-ray spectra observed by SAX in October 1996 and 1997 yields a spectral index 0.74+/-0.07, typical of Seyfert galaxies and consistent with earlier observations of this source. The strong, soft X-ray absorption has column density 1.79E(23)/cm^2, again consistent with earlier results. The best fitting spectrum is that of a power law with a high energy cutoff at 29+/-10 keV, a cold, marginally resolved Fe Kalpha line with EW 290 eV (1996) and a mildly ionized Fe K-edge at 7.37 keV. The Kalpha line and cold absorption are consistent with origin in a accretion disk/torus through which our line-of-sight passes at a radial distance of $\sim 50$ pc. The Fe K-edge is mildly ionized suggesting the presence of ionized gas probably in the inner accretion disk, close to the central source or in a separate warm absorber. The data quality is too low to distinguish between these possibilities but the edge-on geometry implied by the water maser emission favors the former. Comparison with earlier observations of ESO103-G35 shows little/no change in spectral parameters while the flux changes by factors of a few on timescales of a few months. The 2--10 keV flux decreased by a factor of 2.7 between Oct 1996 and Oct 1997 with no detectable change in the count rate >20 keV suggesting a constant or delayed response reflection component. The high energy cutoff is lower than the typical 300keV values seen in Seyfert galaxies. A significant subset of similar sources would affect current models of the AGN contribution to the cosmic X-ray background which generally assume a high energy cutoff of 300 keV.

22 pages, postscript file, accepted for publication in ApJ