  We present a detailed linear, nonadiabatic pulsational scenario for
oscillating Blue Stragglers (BSs)/SX Phoenicis (SX Phe) in Galactic Globular
Clusters (GGCs) and in Local Group (LG) dwarf galaxies. The sequences of models
were constructed by adopting a wide range of input parameters and properly
cover the region of the HR diagram in which these objects are expected to be
pulsationally unstable. Current calculations together with more metal-rich
models already presented by Gilliland et al. suggest that the pulsation
properties of SX Phe are partially affected by metal content. Our calculations
also suggest that the secular period change seems to be a good observable to
identify the pulsation mode of cooler SX Phe variables. The dependence of
pulsation properties on the helium envelope content is discussed and we find
that the secular period change for He-enhanced models is approximately a factor
of two larger than for canonical ones. According to this evidence we suggest
that the pulsation properties of SX Phe can be soundly adopted to constrain the
evolutionary history of BSs, and in turn to single out the physical mechanisms
which trigger their formation.
