On the Theoretical Period-Luminosity Relation of Cepheids
  The theoretical period-luminosity relation for Cepheids was deduced from stellar evolution and pulsation computations. Questions concerning the metallicity dependence of the relation as well as the constancy of the pulsation `constant' Q in the instablility strip were addressed. We found no significant metallicity dependence of either the slope or of the zero-point of the period-luminosity relation. The Q-value, however, varies across the instability strip, in effective temperature as well as in luminosity; its metallicity dependence, on the other hand, is marginal. 
H. Saio and A. Gautschy