New estimates of the distances of 36 nearby galaxies is presented. These are based on the calibration of the V- and I-band Period-Luminosity relations for galactic Cepheids measured by the HIPPARCOS mission. The distance moduli are obtained in a classical way. The statistical bias due to the incompleteness of the sample is corrected according to the precepts introduced by Teerikorpi (\cite{Tee87}). We adopt a constant slope (the one obtained with LMC Cepheids). The correction for incompleteness bias introduces an uncertainty that depends on each galaxy. On average, this uncertainty is small (0.04 mag) but it may reach 0.3 mag. We show that the uncertainty due to the correction of the extinction is small (propably less than 0.05 mag). The correlation between the metallicity and the morphological type of the host galaxy suggests that we should reduce the application to spiral galaxies in order to bypass the problem of metallicity. We suspect that the adopted PL slopes are not valid for all morphological types of galaxies. This may induce a mean systematic shift of 0.1 mag on distance moduli. A comparison with the distance moduli recently published by Freedman et al. (\cite{Fre01}) shows there is a reasonably good agreement with our distance moduli. The compilation of raw data is only available in electronic form at CDS via anonymous ftp to\ cdsarc.u-strasbg.fr (130.79.128.5) or via\ http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/389/19 and on our anonymous ftp-server www-obs.univ-lyon1.fr (pub/base/CEPHEIDES.tar.gz).