  We present the second part of an optical spectroscopic study of planetary
nebulae in the LMC and SMC. The first paper, Leisy & Dennefeld (1996),
discussed the CNO cycle for those objects where C abundances were available. In
this paper we concentrate more on other elemental abundances (such as O, Ne, S,
Ar) and their implications for the evolution of the progenitor stars. We use a
much larger sample of 183 objects, of which 65 are from our own observations,
where the abundances have been re-derived in a homogeneous way. For 156 of
them, the quality of data is considered to be satisfactory for further
analysis. We confirm the difficulty of separating Type-I and non-type-I objects
in the classical He-N/O diagram, as found in Paper I, a problem reinforced by
the variety of initial compositions for the progenitor stars. We observed
oxygen variations, either depletion via the ON cycle in the more massive
progenitor stars, or oxygen production in other objects. Neon production also
appears to be present. These enrichments are best explained by fresh material
from the core or from burning shells, brought to the surface by the 3rd
dredge-up, as reproduced in recent models, some including overshooting. All the
effects appear stronger in the SMC, suggesting a higher efficiency in a low
metallicity environment. Neither oxygen nor neon can therefore be used to
derive the initial composition of the progenitor star: other elements not
affected by processing such as sulfur, argon or, if observed, chlorine, have to
be preferred for this purpose. Some objects with very low initial abundances
are detected, but on average, the spatial distribution of PNe abundances is
consistent with the history of star formation (SF) as derived from field stars
in both Clouds.
