  The determination of accurate chemical abundances of planetary nebulae (PN)
in different galaxies allows us to obtain important constraints of chemical
evolution models for these systems. We have a long term program to derive
abundances in the galaxies of the Local Group, particularly the Large and Small
Magellanic Clouds. In this work, we present our new results on these objects
and discuss their implications in view of recent abundance determinations the
literature. In particular, we obtain distance-independent correlations
involving He, N, O, Ne, S, and Ar, and compare the results with data from our
own Galaxy and other galaxies in the Local Group. As a result of our
observational program, we have a large database of PN in the Galaxy and the
Magellanic Clouds, so that we can obtain reliable constraints to the
nucleosynthesis processes in the progenitor stars in galaxies of different
metallicities.
