Variable precession of the NS in Her X-1

We present evidence for an identical behavior of the precession of the accretion disk and that of the neutron star (NS) in Her X-1, based on investigating the well established 35day modulation in Her X-1 in two different ways: 1) following the turn-ons, thought to be due to the precession of the accretion disk, and 2) following the re-appearance of the shape of the pulse profiles, which we assume to be due to precession of the NS. The turn-on evolution and the evolution of the `phase-zero' values of the precessing NS (as determined from the pulse profiles) track each other very closely. Since the turn-on evolution is strongly correlated with the pulse period evolution, this means that there is also a strong correlation between the spin and the precession of the NS. There is a very strong physical coupling between the NS and the accretion disk, we suggest through physical feedback in the binary system. The apparent long-term stability of the 35 d clock may be due to the `interior' of the NS, the coupling of which to the observable surface effects is of general importance for the physics of super-dense, highly magnetized material.