  The breakdown of Lorentz's and CPT invariance, as described by the Extension
of the Standard Model, gives rise to a modification of the dispersion relation
of particles. Consequences of such a modification are reviewed in the framework
of pulsar kicks induced by neutrino oscillations (active-sterile conversion). A
peculiar feature of the modified energy-momentum relations is the occurrence of
terms of the form $\delta {\bbox \Pi}\cdot {\bf {\hat p}}$, where $\delta
{\bbox \Pi}$ accounts for the difference of spatial components of flavor
depending coefficients which lead to the departure of the Lorentz symmetry, and
${\bf {\hat p}}={\bf p}/p$, being ${\bf p}$ the neutrino momentum. Owing to the
relative orientation of ${\bf p}$ with respect to $\delta {\bbox \Pi}$, the
{\it coupling} $\delta {\bbox \Pi}\cdot {\bf {\hat p}}$ may induce the
mechanism to generate the observed pulsar velocities. Topics related to the
velocity distribution of pulsars are also discussed.
