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We investigate the properties of the so-called BL Her stars, i.e., PopulationII Cepheids with periods shorter than 8 days, using updated pulsation modelsand evolutionary tracks computed adopting a metal abundance in the range ofZ=0.0001 to Z=0.004. We derive the predicted Period-Magnitude (PM) andPeriod-Wesenheit (PW) relations at the various photometric bands and we showthat the slopes of these relations are in good agreement with the slopesdetermined by observed variables in Galactic globular clusters, independentlyof the adopted M_V(RR)-[Fe/H] relation to get the cluster RR Lyrae-baseddistance. Moreover, we show that also the distances provided by the predictedPM and PW relations for BL Her stars agree within the errors with the RR Lyraebased values. The use of the predicted relations with W Vir stars, which arePopulation II Cepheids with periods longer than 8 days, provides no clearevidence for or against a change in the PM and PW slopes around P~10 days.

Synthetic properties of bright metal-poor variables. II. BL Her stars