Context : Aims : Several frequency combinations are widely used in the analysis of stellar oscillations for comparisons between models and observations . In particular , the “ small separations ” can help constraining the 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 . Methods : We computed evolutionary tracks for models with various masses ( from 1.05 to 1.25 M _ { \odot } ) and various chemical compositions , 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 . Results : We find that , for all cases , the stars go through a stage during their evolution , where the small separations computed between degrees \ell = 0 and \ell = 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 interpreting of the acoustic frequencies observed in solar-type stars . Conclusions :