THE isotropy and flat count spectrum of γ-ray bursts revealed by the BATSE detector on the Compton Gamma-Ray Observatory1 have led to suggestions that the burst sources are an extended galactic halo of high-velocity neutron stars2,3We show here that if slow accretion onto these neutron stars from the interstellar medium is to be the origin of γ-ray bursts, the accretion physics is very different from what applies for local, low-velocity neutron stars4,5. For halo neutron stars with high magnetic fields and velocities (v > 190 km s-1), electromagnetic dipole radiation pressure prevents accretion unless the period is longer than tens of seconds; the centrifugal barrier will then prevent accretion until the period reaches several thousand seconds. For periods as long as this, accretion may proceed through Kelvin-Helmholtz instability at the magnetopause boundary. At interstellar densities and neutron-star magnetic fields of ~1012 G, the accretion rate by this process can be much larger than the Bondi-Hoyle (hydrodynamic) accretion rate, but is still well below what is needed for slow-accretion burst models. We conclude that slow accretion onto high-velocity neutron stars in the halo cannot be the origin ofγ-ray bursts.