  Saio et al. (2006) have shown that the presence of an intermediate convective
zone (ICZ) in post-main sequence models could prevent the propagation of
g-modes in the radiative interior and hence avoid the corresponding radiative
damping. The development of such a convective region highly depends on the
structure of the star in the mu-gradient region surrounding the convective core
during the main sequence phase. In particular,the development of this ICZ
depends on physical processes such as mass loss, overshooting (Chiosi & Maeder
1986, Chiosi et al. 1992, see also Godart et al., these proceedings) and
convective instability criterion (Schwarzschild's or Ledoux's criteria). In
this paper we study the consequences of adopting the Ledoux's criterion on the
evolution of the convective regions in massive stars (15 and 20 Msun), and on
the pulsation spectrum of these new B-type variables (also called SPBsg).
