The evolution of Pop I intermediate mass stars is followed from the zero-age main sequence until the early AGB in the presence of convective overshooting from the central cores and mass loss by stellar wind in late stages. Use is made of the determination of Kettner et al. (1982) for the C-12 (alpha, gamma) O-16 reaction rate. Several important consequences are shown to be possible if substantial overshooting occurs in the convective cores of real stars. The new evolutionary models have much larger convective cores and therefore larger He and CO cores than the classical ones. The evolutionary tracks in the H-R diagram run at higher luminosities, and cover a wider range of effective temperatures during the core H-burning phase. However, the extension of the blue loops during the core H-burning phase is strongly reduced. Finally, the mass limits which confine intermediate stars are significantly lowered by the effect of overshooting on critical masses for nondegenerative He and C ignition.
