Previous nonlinear fundamental pulsation models for classical Cepheids with metal content Z \leq 0.02 are implemented with new computations at super-solar metallicity ( Z =0.03 , 0.04 ) and selected choices of the helium-to-metal enrichment ratio \Delta Y / \Delta Z .
On this basis , we show that the location into the HR diagram of the Cepheid instability strip is dependent on both metal and helium abundance , moving towards higher effective temperatures with decreasing the metal content ( at fixed Y ) or with increasing the helium content ( at fixed Z ) .
The contributions of helium and metals to the predicted Period-Luminosity and Period-Luminosity-Color relations are discussed , as well as the implications on the Cepheid distance scale .
We suggest that the adoption of empirical V and I Period-Luminosity relations , as inferred by Cepheids at the Large Magellanic Cloud ( LMC ) , to get distance moduli with an uncertainty of \pm 0.10 mag is fully justified for variables in the short period range ( P \leq 10 days ) , at least with Z \leq 0.04 and \Delta Y / \Delta Z in the range of 2 to 4 .
Conversely , at longer periods ( P > 10 days ) a correction to LMC-based distance moduli may be needed , whose sign and amount depend on the helium and metal content of the Cepheids .
Specifically , from fundamental pulsators with Z > 0.008 we derive that the correction ( in mag ) may be approximated as c = -6.03 + 17.80 Y - 2.80log Z + 8.19 Y log Z , with a total intrinsic uncertainty of \pm 0.05 mag , whereas is c = -0.23 ( \pm 0.03 ) log ( Z / 0.008 ) if Z < 0.008 .
Based on these new results , we show that the empirical metallicity correction suggested by Cepheid observations in two fields of the galaxy M101 may be accounted for , provided that the adopted helium-to-metal enrichment ratio is reasonably high ( \Delta Y / \Delta Z \sim 3.5 ) .

\keywords Stars : variables : Cepheids – Stars : oscillations – Stars : distances