The present invention relates to a solid catalyst component for the polymerization of olefins CH2═CHR in which R is hydrogen or a hydrocarbyl radical with 1-12 carbon atoms, comprising a titanium compound, having at least a Ti-halogen bond and an electron donor compound supported on a Mg halide, in which said electron donor compound is selected from esters of malonic acids of formula (I): wherein R1 is H or a C1-C20 linear or branched alkyl, alkenyl, cycloalkyl, aryl, arylalkyl or alkylaryl group; R2 is a C1-C20 linear or branched alkyl, alkenyl, cycloalkyl, aryl, arylalkyl or alkylaryl group; R3 and R4 the same or different are C4-C20 linear or branched alkyl, alkylcycloalkyl, primary arylalkyl or primary alkylaryl. Said catalyst components when used in the polymerization of olefins, and in particular of propylene, are capable to give high yields and polymers having high insolubility in xylene.