  [Abridged] One of the most outstanding problems related to numerical models
of galaxy formation is the so-called ``angular momentum catastrophe''. We study
the evolution of the angular momentum from z~0.6 to z=0 to further our
understanding of the mechanisms responsible for the large angular momenta of
disk galaxies observed today. This study is based on a complete sample of 32,
0.4<z<0.75 galaxies observed with FLAMES/GIRAFFE at the VLT. Their kinematics
had been classified as rotating disks, perturbed rotators, or complex
kinematics .We have computed the specific angular momentum of disks (j_disk)
and the dynamical support of rotating disks through the V/sigma ratio. To study
how angular momentum can be acquired dynamically, we have compared the
properties of distant and local galaxies. We find that distant rotating disks
have essentially the same properties (j_disk and R_d) as local disks, while
distant galaxies with more complex kinematics have a significantly higher
scatter in the j_disk--V_max and R_d--V_max planes. On average, distant
galaxies show lower values of V/sigma than local galaxies. We found
observational evidence for a non-linear random walk evolution of the angular
momentum in galaxies during the last 8 Gyr. The evolution related to galaxies
with complex kinematics can be attributed to mergers. If galaxies observed at
intermediate redshift are related to present-day spirals, then our results fit
quite well with the ``spiral rebuilding'' scenario proposed by Hammer et al.
(2005)
