  Several glitches have been observed in young, isolated radio pulsars, while a
clear detection in accretion-powered X-ray pulsars is still lacking. We use the
Pizzochero snowplow model for pulsar glitches as well as starquake models to
determine for the first time the expected properties of glitches in accreting
pulsars and their observability. Since some accreting pulsars show
accretion-induced long-term spin-up, we also investigate the possibility that
anti-glitches occur in these stars. We find that glitches caused by quakes in a
slow accreting neutron star are very rare and their detection extremely
unlikely. On the contrary, glitches and anti-glitches caused by a transfer of
angular momentum between the superfluid neutron vortices and the non-superfluid
component may take place in accreting pulsars more often. We calculate the
maximum jump in angular velocity of an anti-glitch and we find that it is
expected to be about 1E-5 - 1E-4 rad/s. We also note that since accreting
pulsars usually have rotational angular velocities lower than those of isolated
glitching pulsars, both glitches and anti-glitches are expected to have long
rise and recovery timescales compared to isolated glitching pulsars, with
glitches and anti-glitches appearing as a simple step in angular velocity.
Among accreting pulsars, we find that GX 1+4 is the best candidate for the
detection of glitches with currently operating X-ray instruments and future
missions such as the proposed Large Observatory for X-ray Timing (LOFT).
