We present stellar evolutionary models covering the mass range from 0.4 to 1M_{sun} calculated for metallicities Z=0.020 and 0.001 with the MHD equation of state (Hummer & Mihalas, 1988ApJ...331..794H, Mihalas et al., 1988ApJ...331..815M, Daeppen et al., 1988ApJ...332..261D). A parallel calculation using the OPAL (Rogers et al., 1996ApJ...456..902R) equation of state has been made to demonstrate the adequacy of the MHD equation of state in the range of 1.0 to 0.8M{sun} (the lower end of the OPAL tables). Below, down to 0.4M{sun}_, we have justified the use of the MHD equation of state by theoretical arguments and the findings of Chabrier & Baraffe (1997A&A...327.1039C). We use the radiative opacities by Iglesias & Rogers (1996ApJ...464..943I), completed with the atomic and molecular opacities by Alexander & Fergusson (1994ApJ...437..879A). We follow the evolution from the Hayashi fully convective configuration up to the redgiant tip for the most massive stars, and up to an age of 20Gyr for the less massive ones. We compare our solar-metallicity models with recent models computed by other groups and with observations.