We investigate the properties of the so-called BL Her stars, i.e., Population
II Cepheids with periods shorter than 8 days, using updated pulsation models
and evolutionary tracks computed adopting a metal abundance in the range of
Z=0.0001 to Z=0.004. We derive the predicted Period-Magnitude (PM) and
Period-Wesenheit (PW) relations at the various photometric bands and we show
that the slopes of these relations are in good agreement with the slopes
determined by observed variables in Galactic globular clusters, independently
of the adopted M_V(RR)-[Fe/H] relation to get the cluster RR Lyrae-based
distance. Moreover, we show that also the distances provided by the predicted
PM and PW relations for BL Her stars agree within the errors with the RR Lyrae
based values. The use of the predicted relations with W Vir stars, which are
Population II Cepheids with periods longer than 8 days, provides no clear
evidence for or against a change in the PM and PW slopes around P~10 days.Comment: 12 pages, 6 figures, 6 tables, accepted for publication in A&A on
date 16/05/200