  Revised Hipparcos parallaxes for classical Cepheids are analysed together
with 10 HST-based parallaxes (Benedict et al.). In a reddening-free V,I
relation we find that the coefficient of logP is the same within the
uncertainties in our Galaxy as in the LMC, contrary to some previous
suggestions. Cepheids in the inner region of NGC4258 with near solar
metallicities (Macri et al.) confirm this result. We obtain a zero-point for
the reddening-free relation and apply it to Cepheids in galaxies used by
Sandage et al. to calibrate the absolute magnitudes of SNIa and to derive the
Hubble constant. We revise their result from 62 to 70+/-5 km/s/Mpc. The
Freedman et al. 2001 value is revised from 72 to 76+/-8 km/s/Mpc. These results
are insensitive to Cepheid metallicity corrections. The Cepheids in the inner
region of NGC4258 yield a modulus of 29.22+/-0.03(int) compared with a
maser-based modulus of 29.29+/-0.15. Distance moduli for the LMC, uncorrected
for any metallicity effects, are; 18.52+/-0.03 from a reddening-free relation
in V,I; 18.47+/-0.03 from a period-luminosity relation at K; 18.45+/-0.04 from
a period-luminosity-colour relation in J,K. Adopting a metallicity correction
in V,I from Marci et al. leads to a true LMC modulus of 18.39+/-0.05.
