  Enigmatic transitions between spin-up and spin-down have been observed in
several X-ray pulsars accreting matter via an accretion disk. In these
transitions, the torque changes sign but remains at nearly the same magnitude.
It has been noted previously that alternating prograde and retrograde disk
flows would explain many features of the torque reversals, although it has been
unclear how a stable retrograde disk could be formed. We suggest that the
reversals may be related to the disk at times being warped to such an extent
that the inner region becomes tilted by more than 90 degrees. This region would
thus become retrograde, leading to a negative torque. Accretion disk models can
show such behavior, if account is taken of a warping instability due to
irradiation. The resulting `flip-overs' of the inner parts of the disk can
reproduce most characteristics of the observations, although it remains unclear
what sets the timescale on which the phenomenon occurs. If this model were
correct, it would have a number of ramifications, for instance that in the
spin-down state the X-ray source would mostly be observed through the accretion
disk.
