The dynamics of relativistically moving blobs ejected out of a central AGN are considered. It is assumed that the collision between two blobs is 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 that are formed by the collision. These high-energy electrons, which are produced on a timescale corresponding to the collision timescale, cool by radiative losses due to synchrotron and inverse Compton processes. The model is applied to the radio/X-ray knots of several AGNs. For three of these sources we have analyzed long (>40 ks) Chandra observations and report on constraints on the X-ray spectral indices. In the framework of this model the AGNs are inferred to sporadically eject relativistic blobs on timescales ranging from 10¹¹ to 10¹² s for different sources. It is shown that the collision timescales can be longer than the age of the knot, and hence nonthermal 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.