  (Abridged) We present numerical simulations of the spectral evolution and
emission of radio components in relativistic jets. We have developed an
algorithm (SPEV) for the transport of a population of non-thermal electrons
including radiative losses. For large values of the ratio of gas pressure to
magnetic field energy density, \ab \sim 6\times 10^4, quiescent jet models show
substantial spectral evolution, with observational consequences only above
radio frequencies. Larger values of the magnetic field (\ab \sim 6\times 10^2),
such that synchrotron losses are moderately important at radio frequencies,
present a larger ratio of shocked-to-unshocked regions brightness than the
models without radiative losses, despite the fact that they correspond to the
same underlying hydrodynamic structure. We also show that jets with a positive
photon spectral index result if the lower limit \gamma_min of the non-thermal
particle energy distribution is large enough. A temporary increase of the
Lorentz factor at the jet inlet produces a traveling perturbation that appears
in the synthetic maps as a superluminal component. We show that trailing
components can be originated not only in pressure matched jets, but also in
over-pressured ones, where the existence of recollimation shocks does not allow
for a direct identification of such features as Kelvin-Helmholtz modes, and its
observational imprint depends on the observing frequency. If the magnetic field
is large (\ab \sim 6\times 10^2), the spectral index in the rarefaction
trailing the traveling perturbation does not change much with respect to the
same model without any hydrodynamic perturbation. If the synchrotron losses are
considered the spectral index displays a smaller value than in the
corresponding region of the quiescent jet model.
