  Dramatic torque reversals between spin up and spin down have been observed in
half of the persistent X-ray pulsars monitored by the BATSE all-sky monitor on
CGRO. Theoretical models developed to explain early pulsar timing data can
explain spin down torques via a disk-magnetosphere interaction if the star
nearly corotates with the inner accretion disk. To produce the observed BATSE
torque reversals, however, these equilibrium models require the disk to
alternate between two mass accretion rates, with $\dot M_{\pm}$ producing
accretion torques of similar magnitude, but always of opposite sign. Moreover,
in at least one pulsar (GX 1+4) undergoing secular spin down the neutron star
spins down faster during brief ($\sim 20$ day) hard X-ray flares -- this is
opposite the correlation expected from standard theory, assuming BATSE pulsed
flux increases with mass accretion rate. The $10$ day to 10 yr intervals
between torque reversals in these systems are much longer than any
characteristic magnetic or viscous time scale near the inner disk boundary and
are more suggestive of a global disk phenomenon.
  We discuss possible explanations of the observed torque behavior. Despite the
preferred sense of rotation defined by the binary orbit, the BATSE observations
are surprisingly consistent with an earlier suggestion by Makishima \etal
(1988) for GX~1+4: the disks in these systems somehow alternate between
episodes of prograde and retrograde rotation. We are unaware of any mechanism
that could produce a stable retrograde disk in a binary undergoing Roche-lobe
overflow, but such flip-flop behavior does occur in numerical simulations of
wind-fed systems. One possibility is that the disks in some of these binaries
are fed by an X-ray excited wind.
