We present the first results on the optical identification of 89 sources with S(0.5-2 keV)>=1.7x10^-14 erg s^-1 cm^-2 detected in eight ROSAT Position Sensitive Proportional Counter (PSPC) observations targeted on the second Lockman hole region. Because of the low Galactic HI column density towards this field [N_HI~(6-12)x10^19 cm^-2] the X-ray spectra of the sources are relatively unaffected by Galactic absorption, and a relation between X-ray spectral properties and the nature of the sources can be established. The optical study is based on R-band CCD images of almost all of the sources, optical spectroscopy of the optically brightest 23 per cent of sources and colour information from the APM measurements of the POSS plates. We find that the fraction of the X-ray sources identified with galaxies is at least 10 per cent. Similarly, a minimum of 29 per cent are QSOs and ~10 per cent are stars. The galaxies form a heterogeneous group of sources, including ellipticals without emission lines, normal star-forming, starburst and Seyfert galaxies. The X-ray spectra of the various types of galaxies are on average significantly harder than those of the QSOs, and similar to those of the stars. This suggests that galaxies may make a significant contribution to the soft X-ray source counts at faint flux levels and in the synthesis of the soft X-ray background.