  The long-term evolution of the relative rotation of the core superfluid in a
neutron star with respect to the rest of the star, at different radial
distances from the rotation axis, is determined through model calculations. The
core superfluid rotates at a different rate (faster, in young pulsars), while
spinning down at the same steady-state rate as the rest of the star, because of
the assumed pinning between the superfluid vortices and the superconductor
fluxoids. We find that the magnitude of this rotational lag changes with time
and also depends on the distance from the rotation axis; the core superfluid
supports an evolving pattern of differential rotation. We argue that the
predicted change of the lag might occur as discrete events which could result
in a sudden rise of the spin frequency of the crust of a neutron star, as is
observed at glitches in radio pulsars. This new possibility for the triggering
cause of glitches in radio pulsars is further supported by an estimate of the
total predicted excess angular momentum reservoir of the core superfluid. The
model seems to offer also resolutions for some other aspects of the
observational data on glitches.
