  The majority of the inhomogeneities in the chemical composition of Globular
Cluster (GC) stars appear due to primordial enrichment. The most studied model
today claims that the ejecta of Asymptotic Giant Branch (AGB) stars of high
mass -those evolving during the first ~100Myr of the Clusters life- directly
form a second generation of stars with abundance anomalies. In this talk, we
review the status of the art with regard to this model, whose major problems
are i) the modelling of the chemical anomalies is still not fully complete, and
ii) it requires an IMF peculiarly enhanced in the intermediate mass stars. The
model predicts enhanced helium abundance in the stars showing chemical
anomalies, and the helium abundance distribution can be roughly derived from
the morphology of the horizontal branch. Such distribution may possibly help to
falsify the model for the first phases of evolution of GCs. As an illustration,
we compare the results of the analysis of the HB morphology of some clusters.
