  A significant number of X-ray binaries are now known to exhibit long-term
``superorbital'' periodicities on timescales of $\sim$ 10 - 100 days. Several
physical mechanisms have been proposed that give rise to such periodicities, in
particular warping and/or precession of the accretion disk. Recent theoretical
work predicts the stability to disk warping of X-ray binaries as a function of
the mass ratio, binary radius, viscosity and accretion efficiency, and here we
examine the constraints that can be placed on such models by current
observations.
  In paper I we used a dynamic power spectrum (DPS) analysis of long-term X-ray
datasets (CGRO, RXTE), focusing on the remarkable, smooth variations in the
superorbital period exhibited by SMC X-1. Here we use a similar DPS analysis to
investigate the stability of the superorbital periodicities in the neutron star
X-ray binaries Cyg X-2, LMC X-4 and Her X-1, and thereby confront stability
predictions with observation. We find that the period and nature of
superorbital variations in these sources is consistent with the predictions of
warping theory.
  We also use a dynamic lightcurve analysis to examine the behaviour of Her X-1
as it enters and leaves the 1999 Anomalous Low State (ALS). This reveals a
significant phase shift some 15 cycles before the ALS, which indicates a change
in the disk structure or profile leading into the ALS.
