  The magnetically decoupled core model was proposed earlier as a way to solve
the problem of inconsistency between the neutron star long-period precession
and superfluid vortex pinning which is the base of most theories of pulsar
glitches. It was assumed that the pinning takes place in the region of the
neutron star core which, being magnetically decoupled, can rotate relative to
the crust. In present work some aspects of the glitch spin-up stage in the
framework of the proposed model are discussed. Estimated spin-up time-scales
are compared with observational data. According to the estimations the Crab
pulsar is likely posses a magnetically decoupling core region, while the
results for the Vela pulsar is more controversial.
