We present the X-ray spectra of 86 optically-identified sources in the 13H XMM-Newton/Chandra deep field which have >70 X-ray counts. The sample consists of 50 broad line AGN, 25 narrow emission line galaxies, 6 absorption line galaxies, and 5 Galactic stars. The majority (42/50) of the broad line AGN have X-ray spectra which are consistent with a power law shape. They have a mean photon index of Gamma = 2.0 +- 0.1 and an intrinsic dispersion sigma = 0.4 +- 0.1. Five BLAGN show a deficit of soft X-rays, indicating absorption. Significant absorption is more common in the narrow emission line galaxies (13/25) and absorption line galaxies (2/6) than in the broad line AGN (5/50), but is not universal in any of these classes of object. The majority of the 20 absorbed sources have X-ray spectra consistent with a simple cold photoelectric absorber, but 6/20 require more complex models with either an additional component of soft X-ray emitting plasma, or an ionised absorber. Of the 16 galaxies which do not show evidence for X-ray absorption, only 2 objects are likely to be powered by star formation, and both have 2-10 keV X-ray luminosities of <= 10^40 cgs. The X-ray emission in the other 14 unabsorbed NELGs and galaxies is most likely powered by AGN, which are not detected in the optical because they are outshone by their luminous host galaxies. The Galactic stars show multi-temperature thermal spectra which peak between 0.5 and 1 keV. Star/AGN discrimination is possible for 4 of the 5 stars solely from their X-ray spectra.
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