Cepheid models based on self-consistent stellar evolution and pulsation calculations: the right answer?

We have computed stellar evolutionary models for stars in a mass range characteristic of Cepheid variables (3 < m/M < 12) for different metallicities representative of the Galaxy and the Magellanic Clouds populations. The stellar evolution calculations are coupled to a linear non adiabatic stability analysis to get self-consistent mass-period-luminosity relations. The period luminosity relation as a function of metallicity is analysed and compared to the recent EROS observations in the Magellanic Clouds. The models reproduce the observed width of the instability strips for the SMC and LMC. We determine a statistical P-L relationship, taking into account the evolutionary timescales and a mass distribution given by a Salpeter mass function. Excellent agreement is found with the SMC PL relationship determined by Sasselov et al. (1997). The models reproduce the change of slope in the P-L relationship near P ∼ 2.5 days discovered recently by the EROS collaboration (Bauer 1997; Bauer et al. 1998) and thus explain this feature in term of stellar evolution. Some discrepancy, however, remains for the LMC Cepheids. The models are also in good agreement with Beat Cepheids observed by the MACHO and EROS collaborations. We show that most of the 1H/2H Beat Cepheids have not yet ignited central helium burning; they are just evolving off the Main Sequence toward the red giant branch.