  Asteroseismology of solar-type stars is an important tool for constraining
stellar parameters and internal structure. Several frequency combinations are
largely used for comparisons between models and observations. In particular,
the ``small separations'' are very sensitive to stellar cores. We showed in a
previous paper that they can change sign, in contradiction with the
``asymptotic theory'', and that this behaviour could correspond to signatures
of convective and/or helium cores. Here we analyse this behaviour in detail by
systematic modelling during stellar evolution. We computed evolutionary tracks
for models with various masses (from 1.05 to 1.25 Msun) and various chemical
composition, with and without overshooting. We computed the adiabatic
oscillation frequencies of the models and analysed the evolution of their small
separations along an evolutionary track. We found that, for all cases, the
stars go through a stage, during their evolution time, where the small
separations computed between degrees l=0 and l=2 become negative in the
observed range of frequencies. This behaviour is clearly related to the
signature of a helium-rich core. We discuss the consequences for the
interpretation of the acoustic frequencies observed in solar-type stars.
