The present invention relates to a solid catalyst component for the polymerization of olefins CH2═CHR in which R is hydrogen or a hydrocarbon radical with 1-12 carbon atoms, comprising Mg, Ti, halogen and an electron donor selected from succinates, said catalyst component being obtainable by a process comprising the following steps: (a) dissolving a halide of magnesium in a solvent system comprising an organic epoxy compound or an organic phosphorus compound and optionally an inert diluent to form a solution; (b) mixing the obtained solution with a titanium compound to form a mixture; (c) precipitating a solid from the mixture obtained in step (b) in the presence of a succinate and/or an auxiliary precipitant; (d) if a succinate is not used in step (c), contacting the solid obtained in (c) with a succinate, and (e) treating the solid obtained in (c) or (d) with a titanium compound optionally in the presence of an inert diluent.