  We have studied the long-term (1971-2005) behaviour of the 1.24 sec pulse
period and the 35 day precession period of Her X-1 and show that both periods
vary in a highly correlated way (see also Staubert et al. 1997 and 2000). When
the spin-up rate decreases, the 35 day turn-on period shortens.This correlation
is most evident on long time scales (~2000 days),e.g.around four extended
spin-down episodes, but also on shorter time scales (a few 100 days) on which
quasi-periodic variations are apparent. We argue that the likely common cause
is variations of the mass accretion rate onto the neutron star.The data since
1991 allow a continuous sampling and indicate a lag between the turn-on
behaviour and the spin behaviour, in the sense that changes are first seen in
the spin, about one cycle later in the turn-on. Both the coronal wind model
(Schandl & Meyer 1994) as well as the stream-disk model (Shakura et al.999)
predict this kind of behaviour.
