  Based on consistent evolutionary and pulsation calculations, we analyse the
effect of metallicity and of different convection treatments in the stellar
models on period - magnitude, - color and - radius relationships. In order to
perform an accurate comparison with observations, we have computed grids of
atmosphere models and synthetic spectra for different metallicities, covering
the range of effective temperatures and gravities relevant for Cepheids. The
models are compared to recent observations of galactic and Magellanic Clouds
Cepheids. Unprecedented level of agreement is found between models and
observations. We show that within the range of metallicity for the Galaxy and
the Magellanic Clouds, a change of slope in the period - luminosity (PL)
relationship is predicted at low periods, due to the reduction of the blue loop
during core He burning. The minimum mass undergoing a blue loop and
consequently the critical period at which this change of slope occurs depend on
the metallicity Z and on the convection treatment in the stellar models.
However, besides this change of slope, we do not find any significant effect of
metallicity on period - magnitude relationships from V to K bands, and on
period - color relationships in IR colors. We only find a detectable effect of
$Z$ on $(B-V)$ colors. These results are not affected by uncertainties inherent
to current stellar models, mainly due to convection treatment.
