  This paper deals with the spectral ageing study of a representative sample of
compact symmetric objects (CSOs) and compact steep spectrum (CSS) sources.
Observations reveal a distinctive high-frequency steepening of the radio
spectra of many of these sources. The existence of such a spectral feature is
expected or may be naturally interpreted in terms of radiative ageing of
synchrotron emitting electrons. The small angular size of CSS sources makes it
relatively easy to measure their integrated spectra over a wide frequency range
for a conspicuous number of objects. For those sources whose emission is
dominated by the mini-lobes, the integrated spectra can be used to constrain
the source age. Assuming equipartition magnetic fields, the spectral ages we
found are in the range from 10^2 to 10^5 yr. Multifrequency VLBA observations
allow us to study the spectral properties of two CSOs: B1323+321 and B1943+546.
The case of B1943+546 is particularly interesting since for this source a
kinematic age has been derived from the proper motion of the hot spots. We
found that spectral and kinematic ages agree within a factor of 2. The overall
results presented here confirm that the CSOs and CSS sources are indeed young
objects. Finally, we show some examples of compact sources characterised by an
extraordinary steep and curved spectrum. It is plausible that these are relic
sources in which the injection of fresh electrons has ceased for a significant
fraction of their lifetime. These observations may indicate either the presence
of intermittent activity or a class of short-living objects.
