  A simple model of cosmic ray electron acceleration at the jet boundary
(Ostrowski 2000) yields a power-law particle energy distribution of
ultrarelativistic electrons with an energy cut-off growing with time and
finally, a growing particle bump at the energy, where energy gains equal
radiation losses. For such electron distribution, in tens-of-kpc scale jets, we
derived the observed time varying spectra of synchrotron and inverse-Compton
radiation, including comptonization of synchrotron and cosmic microwave
background photons. Slowly varying spectral index along the jet in the
`low-frequency' spectral range is a natural consequence of boundary layer
acceleration. Variations of the high energy bump of the electron distribution
can give rise to anomalous behaviour in X-ray band in comparison to the lower
frequencies.
