  The dynamics of relativistically moving blobs ejected out of a central AGN,
are considered. It is assumed that the collision between two blobs are
completely inelastic, such that the bulk kinetic energy lost in the collision
is used to energize electrons to relativistic energies via acceleration in
internal shocks which are formed due to the collision. These high energy
electrons which are produced on a time-scale corresponding to the collision
time-scale, cool by radiative losses due to synchrotron and Inverse Compton
processes. The model is applied to the radio/X-ray knots of several AGN. For
three of these sources we have analyzed long (> 40 ksec) Chandra observations
and report on constrains on the X-ray spectral indices. In the framework of
this model the AGN are inferred to sporadically eject relativistic blobs on
time-scales ranging from 10^{11} to 10^{12} secs for different sources. It is
shown that the collision time-scales can be longer than the age of the knot
and, hence, non-thermal electrons are continuously being injected into the
system. This continuous injection, in contrast to an instantaneous one time
injection, gives rise to a characteristic spectral break, rather than a
high-energy cutoff in the spectrum.
