  Gamma-ray bursts (GRBs) are the most energetic events after the Big Bang and
they have been observed up to very high redshift. By means of measures of
chemical abundances now available for the galaxies hosting such events,thought
to originate from the explosion of very powerful supernovae (Type Ib/c), we
have the opportunity to study the nature of these host galaxies. The aim of
this paper is to identify the hosts of Long GRBs (LGRBs) observed both at low
and high redshift to see whether the hosts can be galaxies of the same type
observed at different cosmic epochs. We adopt detailed chemical evolution
models for galaxies of different morphological type (ellipticals, spirals,
irregulars) which follow the time evolution of the abundances of several
chemical elements (H, He, $\alpha$-elements, Fe), and compare the results with
the observed abundances and abundance ratios in galaxies hosting LGRBs. We find
that the abundances and abundance ratios predicted by models devised for
typical irregular galaxies can well fit the abundances in the hosts both at
high and low redshift. We also find that the predicted Type Ib/c supernova rate
for irregulars is in good agreement with observations. Models for spirals and
particularly ellipticals do not fit the high-redshift hosts of LGRBs (DLA
systems) nor the low redshift hosts: in particular, ellipticals cannot possibly
be the hosts of gamma-ray-bursts at low redshift since they do not show any
star formation, and therefore no supernovae Ib/c. We conclude that the observed
abundance and abundance ratios in LGRBs hosts suggest that these hosts are
irregular galaxies both at high and low redshift thus showing that the host
galaxies belong to in an evolutionary sequence.
