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 } years .
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 .

Throughout this paper we adopt { H _ { 0 } } = 100 h { km s ^ { -1 } Mpc ^ { -1 } } and { q _ { 0 } } = 0.5 .