  The puzzling phenomenon of pulsar kicks, i.e. the observed large escape
velocities of pulsars out of supernova remnants, is examined for compact stars
with a strange quark matter core. The direct Urca process in quark matter is
studied in the presence of a strong magnetic field. Conditions for an
asymmetric emission of the produced neutrinos are worked out in detail, giving
constraints on the temperature, the strength of the magnetic field and the
electron chemical potential in the quark matter core. In addition, the neutrino
mean free paths for quark matter and a possible hadronic mantle are considered.
