  We study the super-orbital modulation present in the Cygnus X-1 X-ray data,
usually attributed to the precession of the accretion disk and relativistic
jets. We find a new, strong, 326+-2 d period modulation starting in 2005, in
Swift/BAT and RXTE/ASM light curves (LCs). We also investigate Vela5B/ASM and
ArielV/ASM archival data and confirm the previously reported ~290 d periodic
modulation, and therefore confirming that the super-orbital period is not
constant. Finally, we study RXTE/ASM LC before 2005 and find that the
previously reported ~150 d period is most likely an artifact due to the use of
a Fourier-power based analysis under the assumption that the modulation has a
constant period along the whole data sample. Instead, we find strong
indications of several discrete changes of the precession period, happening in
coincidence with soft and failed state-transition episodes. We also find a hint
of correlation between the period and the amplitude of the modulation. The
detection of gamma-rays above 100 GeV with MAGIC in September 2006 happened in
coincidence with a maximum of the super-orbital modulation. The next maximum
will happen between 2 and 14 of July 2008, when the observational conditions of
Cygnus X-1 with ground-based Cherenkov telescopes, such as MAGIC and VERITAS,
are optimal.
