  New estimate of the distances of 36 nearby galaxies is presented. It is based
on the calibration of the V- and I-band Period-Lumi- nosity 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
(1987).
  We adopt a constant slope (the one obtained with LMC Cepheids). The
correction for incompleteness bias introduce an uncertainty which depends on
each galaxy. On the mean, this uncertainty is small (0.04 mag) but it may reach
0.3 mag. We show that the un- certainty 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 sug- gests us to
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.
(2001) shows there is a reasonably good agreement with our distance moduli.
