  We consider the acceleration of particles due to a velocity shear in
relativistic astrophysical flows. The basic physical picture and the formation
of power law momentum spectra is discussed for a non-relativistic velocity
field using a microscopic approach. We identify possible sites for shear
acceleration in relativistic astrophysical jets and analyze their associated
acceleration timescales. It is shown in particular that for a mean scattering
time $\tau$ scaling with the gyro-radius, the acceleration timescale for
gradual shear scales in the same manner as the synchrotron cooling timescale,
so that losses may no longer be able to stop the acceleration once it has
started to work efficiently. Finally, the possible role of shear acceleration
is discussed with reference to the relativistic jet in the quasar 3C~273.
