  We analyse a sample of 236 Cepheids from the Hipparcos catalog, using the
method of ``reduced parallaxes'' in V, I, K and the reddening-free
``Wesenheit-index''. We compare our sample to those considered by Feast &
Catchpole (1997) and Lanoix et al. (1999).
  We stress the importance of two systematic effects which influence the
distance to the LMC: the slopes of the Galactic PL-relations and metallicity
corrections. In order to assess the influence of these various effects, we
present 27 distance moduli (DM) to the LMC, based on three different colours
(V,I,K), three different slopes, and three different metallicity corrections.
  The DM to the LMC based on the parallax data can be summarised as follows.
Based on the PL-relation in V and I, and the Wesenheit-index, the DM is 18.60
\pm 0.11 (\pm 0.08 slope)(^{+0.08}_{-0.15} metallicity), which is our current
best estimate.
  Based on the PL-relation in K the DM is 18.52 \pm 0.18$ (\pm 0.03 slope) (\pm
0.06 metallicity)(^{+0.10}_{-0} sampling bias}).
  The random error is mostly due to the given accuracy of the Hipparcos
parallaxes and the number of Cepheids in the respective samples. The terms
between parentheses indicate the possible systematic uncertainties due to the
slope of the Galactic PL-relations, the metallicity corrections, and in the
K-band, due to the limited number of stars. Recent work by Sandage et al.
(1999) indicates that the effect of metallicity towards shorter distances may
be smaller in V and I than indicated here.
