  We investigate the theoretical scenario concerning the large sample of
variables recently discovered in the dwarf, metal-poor irregular galaxy Leo A,
focusing the attention on the "Anomalous" Cepheid phenomenon and its
correlation with RR Lyrae stars, Classical and Population II Cepheids. To this
purpose, we make use of suitable stellar and pulsation models to depict the
pulsational history of evolutionary structures with metallicity Z=0.0004,
finding that He-burning pulsators are expected only outside the mass interval ~
0.8-1.7 Mo. The dependence on metal content of this scenario has been
investigated over the range Z=0.0002 to 0.008. One finds that the edges of the
pulsational strip for the more massive class of pulsators appear independent of
metallicity, but with the minimum mass of these bright pulsators which
decreases when decreasing the metallicity, thus decreasing the predicted
minimum luminosity and period. Comparison with data for Cepheids in Leo A and
in the moderately metal rich extragalactic stellar system Sextans A discloses
an encouraging agreement with the predicted pulsational scenario. On this
basis, we predict that in a stellar system where both RR Lyrae stars and
Cepheids are observed, their magnitude difference may help in constraining both
the metal content and the distance. The current classification of metal-poor
Cepheids is shortly discussed, advancing the suggestion for an updated
terminology abreast of the current knowledge of stellar evolution.
