  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 $\log P$ - $\wi$ (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 $\te$ 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.
