  We present results of an extensive study of the X-ray spectral properties of
sources detected in the RIXOS survey, that is nearly complete down to a flux
limit of 3e-14 cgs (0.5-2 keV). We show that for X-ray surveys containing
sources with low count rate spectral slopes estimated using simple hardness
ratios in the ROSAT band can be biased. Instead we analyse three-colour X-ray
data using statistical techniques appropriate to the Poisson regime which
removes the effects of this bias. We have then applied this technique to the
RIXOS survey to study the spectral properties of the sample. For the AGN we
find an average energy index of 1.05+-0.05 with no evidence for spectral
evolution with redshift. Individual AGN are shown to have a range of properties
including soft X-ray excesses and intrinsic absorption. Narrow Emission Line
Galaxies also seem to fit to a power-law spectrum, which may indicate a
non-thermal origin for their X-ray emission. We infer that most of the clusters
in the sample have a bremsstrahlung temperature >3 keV, although some show
evidence for a cooling flow. The stars deviate strongly from a power-law model
but fit to a thermal model. Finally, we have analysed the whole RIXOS sample
containing 1762 sources. We find that the mean spectral slope of the sources
hardens at lower fluxes in agreement with results from other samples. However,
a study of the individual sources demonstrates that the hardening of the mean
is caused by the appearance of a population of very hard sources at the lowest
fluxes. This has implications for the nature of the soft X-ray background.
