  We study the horizontal branch oscillations (HBO) and the two simultaneous
kilohertz QPOs comparing their properties in five Z sources with the
predictions of the magnetospheric beat-frequency and Lense-Thirring precession
models. We find that the variation of the HBO frequency with accretion rate
predicted by the magnetospheric beat-frequency model for a purely dipolar
stellar magnetic field and a radiation-pressure-dominated inner accretion disk
agrees well with the observed variation. This model implies that the neutron
stars in the Z sources are near magnetic spin equilibrium, that their magnetic
field strengths are ~10^9-10^10 G, and that the critical fastness parameter for
these sources is >0.8. If the frequency of the upper kilohertz QPO is an
orbital frequency in the accretion disk, the magnetospheric beat-frequency
model requires that a small fraction of the gas in the disk does not couple
strongly to the stellar magnetic field at 3-4 stellar radii but instead drifts
slowly inward in nearly circular orbits until it is within a few kilometers of
the neutron star surface. The Lense-Thirring precession model is consistent
with the observed magnitudes of the HBO frequencies only if the moments of
inertia of the neutron stars in the Z sources are 4-5 times larger than the
largest values predicted by realistic neutron-star equations of state. The
trend of the correlation between the HBO and upper kHz QPO frequencies is not
consistent with this model. We argue that the change in the slope of the
correlation between the frequency of the horizontal branch oscillation and the
frequency of the upper kilohertz QPO, when the latter is greater than 850 Hz,
is directly related to the varying frequency separation of the kilohertz QPOs.
