A Prepolymerized catalyst component for the polymerization of olefins comprising a solid catalyst component which comprises Mg, Ti, and chlorine atoms and an electron donor (ID) said prepolymerized catalyst component being characterized by the fact that: the electron donor (ID) is constituted by at least 80% mol of 1,3 diethers with respect to the total molar amount of electron donor compounds; the prepolymerized catalyst has a porosity due to pores with diameters up to 1 μm of less than 0.2 cm3/g; it contains an amount of ethylene prepolymer of less than 45% with respect to the total weight of prepolymerized catalyst.