We present the results of evolutionary computations devoted to a study of the effect of a nonvanishing neutrino magnetic moment (n.m.m.) on the evolution of stars. In agreement with previous investigations, we found that n.m.m affects the evolution of low-mass stars, increasing the cooling mechanisms in the core of red giants and thus increasing the mass M c of the He core at the onset of central He burning. One finds that in the range 0<μ ν <10 −11 μ B (Bohr magnetons), M c appears linearly dependent on the value of μ ν