  We test whether the peak absolute magnitude Mv(TO) of the Globular Cluster
Luminosity Function (GCLF) can be used for reliable extragalactic distance
determinations. Starting with the luminosity function of the Galactic Globular
Clusters listed in Harris catalog, we determine Mv(TO) either using current
calibrations of the absolute magnitude Mv(RR) of RR Lyrae stars as a function
of the cluster metal content [Fe/H] and adopting selected cluster samples. We
show that the peak magnitude is slightly affected by the adopted Mv(RR)-[Fe/H]
relation, while it depends on the criteria to select the cluster sample. As for
the GCLFs in other external galaxies, using Surface Brightness Fluctuations
(SBF) measurements we give evidence that the luminosity functions of the blue
(metal-poor) Globular Clusters peak at the same luminosity within ~0.2 mag,
whereas for the red (metal-rich) samples the agreement is within ~0.5 mag even
accounting for the theoretical metallicity correction expected for clusters
with similar ages and mass distributions. Then, using the SBF absolute
magnitudes provided by a Cepheid distance scale calibrated on a fiducial
distance to LMC (m(LMC)=18.50 mag), we show that the Mv(TO) value of the
metal-poor clusters in external galaxies(-7.67+/-0.23 mag) is in excellent
agreement with the value of both Galactic (-7.66+/-0.11 mag) and M31
(-7.65+/-0.19 mag)ones.
