  The long-period ($P = 1091$ s) of the recently discovered pulsar GLEAM-X
J162759.5-523504.3 can be attained by neutron stars evolving with fallback
discs and magnetic dipole moments of a few $10^{30}$ G cm$^3$ at ages greater
than $\sim 2 \times 10^5$ yr consistently with the observational upper limits
to the period derivative, $\dot{P}$, and the X-ray luminosity, $L_X$, of the
source. The current upper limits for $\dot{P}$ allow two alternative present
states: (1) The disc is still active with ongoing accretion at a low rate such
that the accretion luminosity is much less than the neutron star's cooling
luminosity, which in turn is below the upper limit for $L_X$. In this scenario
the spin-down will continue at $\dot{P} \sim 10^{-10}$ s s$^{-1}$ until the
disc becomes inactive; the final period will be $P \sim$ a few $10^3$ s. (2)
The disc is already inactive, there is no accretion. In this case the period
evolution has leveled off to the observed value in the final period range. The
remaining, very weak, dipole torque sustaining asymptotic spin-down at $\dot{P}
\sim 4 \times 10^{-18}$ s s$^{-1}$. Long periods $P \sim$ a few $10^3$ s were
predicted for the final states of soft gamma repeaters and anomalous X-ray
pulsars with relatively strong dipole fields in earlier work with the fallback
disc model.
