Context : The universality of the Cepheid Period-Luminosity relations has been under discussion since metallicity effects have been assumed to play a role in the value of the intercept and , more recently , of the slope of these relations .

Aims : The goal of the present study is to calibrate the Galactic PL relations in various photometric bands ( from B to K ) and to compare the results to the well-established PL relations in the LMC .

Methods : We use a set of 59 calibrating stars , the distances of which are measured using five different distance indicators : Hubble Space Telescope and revised Hipparcos parallaxes , infrared surface brightness and interferometric Baade-Wesselink parallaxes , and classical Zero-Age-Main-Sequence-fitting parallaxes for Cepheids belonging to open clusters or OB stars associations .
A detailed discussion of absorption corrections and projection factor to be used is given .

Results : We find no significant difference in the slopes of the PL relations between LMC and our Galaxy .

Conclusions : We conclude that the Cepheid PL relations have universal slopes in all photometric bands , not depending on the galaxy under study ( at least for LMC and Milky Way ) .
The possible zero-point variation with metal content is not discussed in the present work , but an upper limit of 18.50 for the LMC distance modulus can be deduced from our data .