Catalyst-forming components and catalysts for the polymerization of olefins based on said components are disclosed. The catalysts comprise the reaction product of: (a) an Al alkyl compound; (b) a silicon compound containing at least a Si—OR or Si—OCOR or Si—NR2 bond, R being a hydrocarbyl radical; and (c) a solid comprising, as essential support, a Mg dihalide in active form and, supported thereon, a Ti halide or a halo-Ti-alcoholate or said halogenated Ti compound and a silicon compound as defined in (b) in a molar ratio with the supported Ti compound from 1.0 mole to 5 moles of silicon compound per mole of Ti compound. The present invention refers to new supported components of catalysts for the polymerization of CH2═CHR olefins wherein R is an alkyl radical with 1 to 4 carbon atoms, or an aryl radical, and mixtures of said olefins with ethylene, and to the catalysts obtained from said components.