Catalyst component for the polymerization of olefins comprising Mg. Ti and an electron donor belonging to mercaptoester derivatives of specific formula (I) in which Z is selected from C, Si, O, N, S or P with the proviso that the atoms O, S, P and N are not directly linked to either the carboxylic group or the sulphur atom of formula (I), the R 2 groups, equal to or different from each other, are hydrogen or a C 1 -C 20 hydrocarbon radicals, optionally containing a heteroatom selected from halogen, P, S, N,O and Si, which can be fused together to form one or more cycles, m is a number satisfying the valences of Z and n is an integer ranging from 1 to 10, X is O or S, Y is -OR 3 , -NR 4 R 5 ) or R 6 groups in which R 1 and R 3 are selected from C 1 -C 15 hydrocarbon groups, optionally containing a heteroatom selected from halogen, P, S, N,O, and Si, R 4 -R 5 groups, independently, are hydrogen or R 1 groups and R 6 groups have the same meaning as R 1 groups.