  This is the second paper in a series studying the photometric and
spectroscopic properties of galaxies of different luminosities in the Coma
cluster. The sample selection, spectroscopic observations and completeness
functions are presented here. To study the spectral properties of galaxies as a
function of their local environment, two fields were selected for spectroscopic
observations to cover both the core (Coma1) and outskirts (ie. south-west of
the core and centered on NGC4839)- (Coma3) of the cluster. Medium resolution
spectroscopy (6-9 \AA) was carried out for a total of 490 galaxies in both
fields (302 in Coma1 and 188 in Coma3), using the WYFFOS multi-fiber
spectrograph on the William Herschel Telescope. The galaxies cover a range of
$12 < R < 20$, corresponding to -23 < M_R < -15 (H0=65 km/sec/Mpc). The
redshifts are measured with an accuracy of 100 km/sec. The spectral line
strengths and equivalent widths are also measured for the same galaxies and
analysed in Poggianti et al (2001- paper III). A total of 189 (Coma1) and 90
(Coma3) galaxies are identified as members of the Coma cluster. An analysis of
the colors show that only two members of the Coma cluster in our sample have
B-R > 2. The completeness functions for the spectroscopic sample is presented.
