  This paper is part of a series devoted to the study of the stellar
populations in brightest cluster galaxies (BCGs), aimed at setting constraints
on the formation and evolution of these objects. We have obtained high
signal-to-noise ratio, long-slit spectra of 49 BCGs in the nearby Universe.
Here, we derive Single Stellar Population (SSP)-equivalent ages, metallicities
and alpha-abundance ratios in the centres of the galaxies using the Lick/IDS
system of absorption line indices. We systematically compare the indices and
derived parameters for the BCGs with those of large samples of ordinary
elliptical galaxies in the same mass range. We find no significant differences
between the index-velocity dispersion relations of the BCG data and those of
normal ellipticals, but we do find subtle differences between the derived
SSP-parameters. The BCGs show, on average, higher metallicity ([Z/H]) and
alpha-abundance ([E/Fe]) values. We analyse possible correlations between the
derived parameters and the internal properties of the galaxies (velocity
dispersion, rotation, luminosity) and those of the host clusters (density,
mass, distance from BCG to X-ray peak, presence of cooling flows), with the aim
of dissentangling if the BCG properties are more influenced by their internal
or host cluster properties. The SSP-parameters show very little dependence on
the mass or luminosity of the galaxies, or the mass or density of the host
clusters. Of this sample, 26 per cent show luminosity-weighted ages younger
than 6 Gyr, probably a consequence of recent - if small - episodes of star
formation. In agreement with previous studies, the BCGs with intermediate ages
tend to be found in cooling-flow clusters with large X-ray excess.
