  Population II pulsatingvariables play a relevant role both as distance
indicators and as tracers of the properties of old stellar populations. In this
paper we present an update and homogeneous pulsational scenario for a wide
range of stellar parameters typical of BL Her stars i.e., Population II
Cepheids with periods shorter than 8 days. To this purpose, we adopt a
nonlinear convective hydrodinamical code evaluate the stability and full
amplitude behaviour of an extensive set of BL Her pulsation models. Various
assumptions of mass, luminosity and metallicity consistent with the most recent
evolutionary prescriptions, are adopted. We obtain the theoretical instability
strip for both fundamental and first overtone pulsators and present a detailed
atlas of light/radial-velocity curves. Some relations for the boundaries of the
instability strip and for the dependence of the absolute magnitude on period,
mass and color, as well as the fundamental period-amplitude relations are
derived.Finally, we provide the theoretical period-radius relation for BL Her
and find that it is in excellent agreement with the empirical relation by Burki
& Meylan and consistent with the one holding for shorter periods for RR Lyrae
stars.
