  We have obtained deep spectra of 26 planetary nebulae (PNe) and 9 compact HII
regions in the nearby spiral galaxy NGC 300, and analyzed them together with
those of the giant HII regions previously observed. We have determined the
physical properties of all these objects and their He, N, O, Ne, S and Ar
abundances in a consistent way.
  We find that, globally, compact HII regions have abundance ratios similar to
those of giant HII regions, while PNe have systematically larger N/O ratios and
similar Ne/O and Ar/O ratios. We demonstrate that the nitrogen enhancement in
PNe cannot be only due to second dredge-up in the progenitor stars, since their
initial masses are around 2--2.5\,\msun. An extra mixing process is required,
perhaps driven by stellar rotation.
  Concerning the radial abundance distribution, PNe behave differently from HII
regions: in the central part of the galaxy their average O/H abundance ratio is
0.15 dex smaller. Their abundance dispersion at any galactocentric radius is
significantly larger than that shown by HII regions and many of them have O/H
values higher than HII regions at the same galactocentric distance. This
suggests that not only nitrogen, but also oxygen is affected by nucleosynthesis
in the PN progenitors, by an amount which depends at least on the stellar
rotation velocity and possibly other parameters. The formal O/H, Ne/H and Ar/He
abundance gradients from PNe are significantly shallower that from HII regions.
We argue that this indicates a steepening of the metallicity gradient in NGC
300 during the last Gyr, rather than an effect of radial stellar motions,
although the large observed dispersion makes this conclusion only tentative.
