We consider stellar evolution in low mass stars (1–3 Mo) near the main sequence with the hypothesis that mild turbulence is present within the all star. Turbulent transport of the elements is modeled by diffusion equations where the diffusion coefficient is chosen to be D = R✶eν where ν is the kinematical viscosity and R✶e is a Reynolds number. We consider the effects of the growth of the gradient of the mean molecular weight on turbulence. The main consequences of diffusion on stellar evolution are (1) an increase of the life time near the main sequence and (2) a change of the radial distributions of chemical species (12C, 13C, 14N, 160) (figure 1). The inhibition of the turbulence, when the gradient of mean molecular weight reaches a certain critical value, allows the evolution towards the red giant branch. When stars evolve towards the giant branch, chemical species are dredged up to the surface. At this stage models with and without diffusion, predict substantially different surface abundances (in particular the 12C/13C and C/N ratios). Comparison between models and the available data on giants during the first dredge-up show that abundance anomalies can be explained if turbulent mixing is present during the main sequence phase (figure 2).