  The ROSAT Deep Survey includes a complete sample of 50 X-ray sources with
fluxes in the $0.5 - 2$ keV band larger than 5.5 $10^{-15}$ erg cm$^{-2}$
s$^{-1}$ in the Lockman field (Hasinger et al., Paper I). We have obtained deep
broad-band CCD images of the field and spectra of many optical objects near the
positions of the X-ray sources. We define systematically the process leading to
the optical identifications of the X-ray sources. For this purpose, we
introduce five identification (ID) classes that characterize the process in
each case. Among the 50 X-ray sources, we identify 39 AGNs, 3 groups of
galaxies, 1 galaxy and 3 galactic stars. Four X-ray sources remain unidentified
so far; two of these objects may have an unusually large ratio of X-ray to
optical flux.
  Keywords: surveys -- galaxies: active -- quasars: emission lines -- galaxies:
Seyfert -- X-rays: galaxies
