The present invention relates to MgCl.sub.2.mROH.nH.sub.2 O adducts, where R is a C.sub.1 -C.sub.10 alkyl, 2.ltoreq.m.ltoreq.4.2, 0.ltoreq.n.ltoreq.0.7, characterized by an X-ray diffraction spectrum in which, in the range of 2.theta. diffraction angles between 5.degree. and 15.degree., the three main diffraction lines are present at diffraction angles 2.theta. of 8.8.+-.0.2.degree., 9.4.+-.0.2.degree. and 9.8.+-.0.2.degree., the most intense diffraction lines being the one at 2.theta.=8.8.+-.0.2.degree., the intensity of the other two diffraction lines being at least 0.2 times the intensity of the most intense diffraction line. Catalyst components obtained from the adducts of the present invention are capable to give catalysts for the polymerization of olefins characterized by enhanced activity and stereospecificity with respect to the catalysts prepared from the adducts of the prior art.