Period -magnitude relationships in

We present theoretical period -magnitude relationships for Cepheids in different filters for fundamental and first overtone pulsators, completing the work by Alibert et al. ([CITE]). 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 P1/P0 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 $\log P$ -WI (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 Teff yields up to 0.45 mag effect on MV 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 -MK relationship, we derive a distance modulus for the LMC in agreement with the value based on WI data