  This is an investigation of the period-luminosity relation of classical
Cepheids in samples of different metallicity. It is based on 481 Cepheids in
the Large and Small Magellanic Clouds from the blue and red filter CCD
observations (most similar to V_J & R_J) of the French EROS microlensing
project. The data-set is complete and provides an excellent basis for a
differential analysis between LMC and SMC. In comparison to previous studies of
effects on the PL-relation, the EROS data-set offers extremely well-sampled
light curves and well-filled instability strips. This allows reliable
separation of Cepheids pulsating in the fundamental and the first overtone mode
and derivation of differential reddening. Our main result concerns the
determination of distances to galaxies which are inferred by using the LMC as a
base and using two color photometry to establish the amount of reddening. We
find a zero-point offset between SMC and LMC which amounts to a difference
between inferred and true distance modulus of 0.14 \pm 0.06 mag in the VI_c
system. The offset is exactly the same in both sets of PL-relations - of the
fundamental and of the first overtone mode Cepheids. No effect is seen on the
slopes of the PL-relations, although the fundamental and the first overtone
mode Cepheids have different PL slopes. We attribute the color and the
zero-point offset to the difference in metallicity between the SMC and LMC
Cepheids. A metallicity effect of that small magnitude still has important
consequencies for the inferred Cepheid distances and the determination of H_0.
When applied to recent estimates based on HST Cepheid observations, our
metallicity dependence makes the low-H_0 values (Sandage et al. 1994) higher
and the high-H_0 values (Freedman et al. 1994b) lower, thus bringing those
