  We use parallax data from the Gaia second data release (GDR2), combined with
parallax data based on Hipparcos and HST data, to derive the
period-luminosity-metallicity (PLZ) relation for Galactic classical cepheids
(CCs) in the V,K, and Wesenheit WVK bands. An initial sample of 452 CCs are
extracted from the literature with spectroscopically derived iron abundances.
Reddening values, pulsation periods, and mean magnitudes are taken from the
literature.
  Based on nine CCs with a goodness-of-fit (GOF) statistic <8 and with an
accurate non-Gaia parallax, a parallax zero-point offset of -0.049 +- 0.018 mas
is derived. Selecting a GOF statistic <8 removes about 40\% of the sample most
likely related due to binarity. Excluding first overtone and multi-mode
cepheids and applying some other criteria reduces the sample to about 200
stars.
  The derived PL(Z) relations depend strongly on the parallax zero-point
offset. The slope of the PL relation is found to be different from the
relations in the LMC at the 3 sigma level. Fixing the slope to the value found
in the LMC leads to a distance modulus (DM) to the LMC of order 18.7 mag,
larger than the canonical distance. The canonical DM of around 18.5 mag would
require a parallax zero-point offset of order $-0.1$ mas.
  Given the strong correlation between zero point, period and metallicity
dependence of the PL relation, and the parallax zero-point offset there is no
evidence for a metallicity term in the PLZ relation.
  The GDR2 release does not allow us to improve on the current distance scale
based on CCs. The value of and the uncertainty on the parallax zero-point
offset leads to uncertainties of order 0.15 mag on the distance scale. The
parallax zero-point offset will need to be known at a level of 3 microas or
better to have a 0.01 mag or smaller effect on the zero point of the PL
relation and the DM to the LMC.
