  We present an investigation of Cepheid distances using theory and
observations. Cepheid models indicate that the slope of the Period-Luminosity
(P-L) relation covering the entire period range (0.40<= logP <=2.0) becomes
steeper when moving from optical to NIR bands, and that the metallicity
dependence of the slope decreases from the B- to the K-band. We estimated V-
and I-band slopes for 87 Cepheid data sets belonging to 48 external galaxies
with nebular oxygen abundance 7.5<= 12+log (O/H) <=8.9. By using Cepheid
samples including more than 20 Cepheids, the chi^2 test indicates that the
hypothesis of a steepening of the P-L_{V,I} relations with increased
metallicity can be discarded at the 99% level. On the contrary, the observed
slopes agree with the metallicity trend predicted by pulsation models, i.e. the
slope is roughly constant for galaxies with 12+log (O/H) < 8.17 and becomes
shallower in the metal-rich regime, with a confidence level of 62% and 92%,
respectively. The chi^2 test concerning the hypothesis that the slope does not
depend on metallicity gives confidence levels either similar (P-L_V, 62%) or
smaller (P-L_I, 67%). We found that the slopes of optical and NIR
Period-Wesenheit (P-W) relations in external galaxies are similar to the slopes
of LMC. On this ground, the P-W relations provide robust distances relative to
the LMC, but theory and observations indicate that the metallicity dependence
of the zero-point in the different passbands has to be taken into account. We
compared the galaxy distances provided by Rizzi et al. (2007) using the TRGB
with our set of Cepheid distances based on the P-W relations. We found that the
metallicity correction on distances based on the P-WBV relation is
gamma_(B,V)=-0.52 mag dex^-1, whereas it is vanishing for the distances based
on the P-WVI and on the P-WJK relations. These findings fully support Cepheid
theoretical predictions.
