We present theoretical period - magnitude relationships for Cepheids in different filters for fundamental and first overtone pulsators , completing the work by Alibert et al .
( 1999 ) .
The results are provided for different metallicities characteristic of the Magellanic Clouds and the Milky Way .
In contrast to the fundamental mode , we find a small metallicity effect on the period - luminosity relationship for the first overtone , due to the sensitivity of the period ratio P _ { 1 } / P _ { 0 } with metallicity .
Comparison is made with observations from OGLE and EROS in the Small and Large Magellanic Clouds .
We emphasize the constraint on theoretical predictions provided by the combination of both fundamental and first overtone observed sequences .
We obtain excellent agreement between models and data in a \log P - W _ { I } ( Wesenheit index ) diagram for a distance modulus for the LMC \mu _ { 0 } = 18.60 - 18.70 .
We analyse the uncertainties of the fundamental period - magnitude relationships and the consequences on distance determination .
We show that an arbitrary shift of the instability strip by 350 K in T _ { eff } yields up to 0.45 mag effect on M _ { V } at a given period , whereas the effect is less than 0.1 mag in the K -band .
Using recent near-IR observations in the Large Magellanic Cloud and our P - M _ { K } relationship , we derive a distance modulus for the LMC in agreement with the value based on W _ { I } data .