  We have explored, in the general framework of the ``young source'' scenario,
evolutionary models for GHz Peaked Spectrum (GPS) galaxies and quasars which
reproduce the observed counts, redshift and peak frequency distributions of
currently available samples. Substantially different cosmological evolution
properties are found for the two populations: the quasar luminosity function
must evolve strongly up to $z\sim 1$, while the data on galaxies may be
consistent with no evolution. The models show that GPS sources (mostly quasars)
may comprise quite a significant fraction of bright ($S> 1 $Jy) radio sources
at $\nu \geq 30 $GHz if the intrinsic distribution of peak frequencies extends
up to $\sim 1000 $GHz. In any case, however, their fraction decreases rapidly
with decreasing flux and their contribution to small scale fluctuations in the
frequency range covered by the forthcoming space missions MAP and Planck
Surveyor is expected to be minor.
