  The nature of the 5-12 s "anomalous" X-ray pulsars remains a mystery. Among
the models that have been proposed to explain the properties of AXPs, the most
likely ones are: (1) isolated accreting neutron stars evolved from the
Thorne-\.{Z}ytkow objects due to complete spiral-in during the common envelope
evolution of high-mass X-ray binaries, and (2) magnetars, which are neutron
stars with ultra-high ($\sim 10^{14}-10^{15}$ G) surface magnetic fields. We
have critically examined the predicted change of neutron star's spin in the
accretion model, and found that it is unable to account for the steady
spin-down observed in AXPs. A simple analysis also shows that any accretion
disk around an isolated neutron star has extremely limited lifetime. A more
promising explanation for such objects is the magnetar model.
