Abstract.We have studied the long-term 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 and2000). 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 spindown 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. 1999) predict this kind of behaviour.