  The acceleration of energetic particles in astrophysical shear flows is
analyzed. We show that in the presence of a non-relativistic gradual velocity
shear, power law particle momentum distributions $f(p) \propto p^{-(3+\alpha)}$
may be generated, assuming a momentum-dependent scattering time $\tau \propto
p^{\alpha}$, with $\alpha > 0$. We consider possible acceleration sites in
astrophysical jets and study the conditions for efficient acceleration. It is
shown, for example, that in the presence of a gradual shear flow and a
gyro-dependent particle mean free path, synchrotron radiation losses no longer
stop the acceleration once it has started to work efficiently. This suggests
that shear acceleration may naturally account for a second, non-thermal
population of energetic particles in addition to a shock-accelerated one. The
possible relevance of shear acceleration is briefly discussed with reference to
the relativistic jet in the quasar 3C 273.
