A sample of 37 Galactic, 10 LMC and 6 SMC cepheids is compiled for which individual metallicity estimates exist and BVIK photometry in almost all cases. The Galactic cepheids all have an individual distance estimate available. For the MC objects different sources of photometry are combined to obtain improved periods and mean magnitudes. A multi-parameter Period-Luminosity relation is fitted to the data which also solves for the distance to the LMC and SMC. When all three galaxies are considered, without metallicity effect, a significant quadratic term in log P is found, as previously observed and also predicted in some theoretical calculations. For the present sample it is empirically determined that for log P < 1.65 linear PL-relations may be adopted, but this restricts the sample to only 4 LMC and 1 SMC cepheid. Considering the Galactic sample a metallicity effect is found in the zero point in the VIWK PL-relation (-0.6 &PLUSMN; 0.4 or -0.8 &PLUSMN; 0.3 mag/dex depending on the in- or exclusion of one object), in the sense that metal-rich cepheids are brighter. The small significance is mostly due to the fact that the Galactic sample spans a narrow metallicity range. The error is to a significant part due to the error in the metallicity determinations and not to the error in the fit. Including the 5 MC cepheids broadens the observed metallicity range and a metallity effect of about -0.27 &PLUSMN; 0.08 mag/dex in the zero point is found in VIWK, in agreement with some previous empirical estimates, but now derived using direct metallicity determinations for the cepheids themselves.