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Context: We present the physical and chemical properties of intermediate-massstars 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 6x 10^{-4}, the models previously computed for chemistries typical of GlobularClusters of an intermediate metallicity (Z=0.001), and for the most metal-richclusters found in our Galaxy (Z=0.004); the main goal is to test theself-enrichment scenario also for metal poor Globular Clusters  Methods: We calculated three grids of intermediate-mass models withmetallicities Z=10^{-4}, 2x10^{-4}, and 6x10^{-4}; the evolutionary sequencesare followed from the pre-main sequence throughout the AGB phase, almost untilthe ejection of the whole envelope. We discuss the chemistry of the ejecta, andin particular the mass fractions of those elements that have been investigatedduring the many, deep, spectrocopic surveys of Globular Clusters  Results: Although the data for oxygen and sodium are scarce for lowmetallicity Globular Clusters, the few data for the unevolved stars in NGC6397are compatible with the models. Further, we find good agreement with the C--Nanticorrelation of unevolved stars in the cluster M15. In this cluster,however, no stars having low oxygen ([O/Fe] = -1) have been detected. The mostmassive, very metal poor clusters, should contain such stars, according to thepresent models. At the lowest metallicity Z=10^{-4}, the ejecta of the mostmassive AGBs have C/O>1, due to the dramatic decrease of the oxygen abundance.We discuss the possible implications of this prediction.

Massive AGB models of low metallicity: the implications for the self-enrichment scenario in metal poor Globular Clusters