  Context: We present the physical and chemical properties of intermediate-mass
stars models of low metallicity, evolved along the thermal pulse phase.
  Aims: The target of this work is to extend to low metallicities, Z=1,2 and 6
x 10^{-4}, the models previously computed for chemistries typical of Globular
Clusters of an intermediate metallicity (Z=0.001), and for the most metal-rich
clusters found in our Galaxy (Z=0.004); the main goal is to test the
self-enrichment scenario also for metal poor Globular Clusters
  Methods: We calculated three grids of intermediate-mass models with
metallicities Z=10^{-4}, 2x10^{-4}, and 6x10^{-4}; the evolutionary sequences
are followed from the pre-main sequence throughout the AGB phase, almost until
the ejection of the whole envelope. We discuss the chemistry of the ejecta, and
in particular the mass fractions of those elements that have been investigated
during the many, deep, spectrocopic surveys of Globular Clusters
  Results: Although the data for oxygen and sodium are scarce for low
metallicity Globular Clusters, the few data for the unevolved stars in NGC6397
are compatible with the models. Further, we find good agreement with the C--N
anticorrelation of unevolved stars in the cluster M15. In this cluster,
however, no stars having low oxygen ([O/Fe] = -1) have been detected. The most
massive, very metal poor clusters, should contain such stars, according to the
present models. At the lowest metallicity Z=10^{-4}, the ejecta of the most
massive AGBs have C/O>1, due to the dramatic decrease of the oxygen abundance.
We discuss the possible implications of this prediction.
