Using a sample of 63 active galactic nuclei (AGN) extracted from the Einstein Extended Medium Sensitivity Survey (EMSS), we study the X-ray spectral properties of X-ray-selected AGN in the 0.1-2.4 keV ROSAT band. These objects are all the EMSS AGN detected with more than 300 net counts in ROSAT Position Sensitive Proportional Counter (PSPC) images available from the public achive (as of 1995 May 31). A Kolmogorov-Smirnov test on the redshift and luminosity distributions shows that this subsample is representative of the whole EMSS sample. For the 21 sources detected with less than 600 net counts we characterize the spectrum using only the hardness ratio technique. For the other 42 sources we obtain a detailed spectral analysis, fitting the data with two different power-law models: one with N-H fixed at the Galactic value and one with N-H as a free parameter. Eight sources (similar to 20 per cent) show a significant deviation from a power law absorbed by Galactic N-H, indicating soft excess (five sources) or excess absorption (three sources). These eight sources are analysed and discussed separately and are excluded from the sample used to study the mean X-ray spectral properties of the EMSS sources. A maximum likelihood (ML) analysis is used to find the mean power-law spectral index [a(p)] and the intrinsic dispersion sigma(p). We find [alpha(p)] = 1.42 with sigma(p) = 0.44. This value is significantly steeper (Delta alpha similar to 0.4) than the mean Einstein IPC spectral index obtained by applying the ML analysis to the whole sample of EMSS AGN. This result shows that the soft excess already noted in optically selected AGN is present also in X-ray-selected AGN. The relatively high value obtained for the intrinsic dispersion confirms that, in the soft band, AGN are characterized by a variety of spectral indices, and the increase with respect to the results obtained from the analysis of Einstein data (Delta sigma(p) similar to 0.16) suggests a further broadening of the spectral index distribution as one moves to softer energies. A comparison between the mean spectral indices of radio-quiet (RQ) and radio-loud (RL) subsamples shows that the mean index of the RL sample is flatter than that of the RQ sample, both in the IPC (Delta alpha similar to 0.3) and in the PSPC (Delta alpha similar to 0.4) data. This suggests that the additional X-ray component in RL AGN dominates the X-ray emission of RL AGN over almost two decades of energy (similar to 0.1-10 keV). Finally, we find no significant correlation between the spectral index alpha(x) and other physical parameters such as redshift, optical luminosity and X-ray luminosity.