A continuous multi-stage process for the production of a propylene-ethylene block copolymer comprises: (i) in a first polymerization stage, directed mainly to the polymerization of propylene, continuously polymerizing propylene, alone or in admixture with ethylene, in the presence of a stereoregular catalyst comprising (A) a titanium-containing solid catalyst component combined with (B) an organoaluminium compound of the formula Al(R²) m X 3-m (in which R² is a C₁-C₂₀ hydrocarbyl group, X is a halogen atom and m is a number from l.5 to 3), and an inert organic solvent or propylene as solvent; and (ii) in a second polymerization stage, continuously polymerizing ethylene, alone or in admixture with propylene, in the presence of the polymerization reaction mixture from the first stage after partial inactivation of the stereoregular catalyst; the first polymerization stage being carried out in two or more polymerization vessels connected in series and using a propylene/ethylene feed containing from 0 to 5% by weight of ethylene, based on the total of propylene and ethylene, to produce from 60 to 95% by weight of the final polymerization product;
the stereoregular catalyst being partially inactivated by addition thereto of a glycol ether (C) in an amount such that the ratio (mole/atom) of moles of glycol to atoms of titanium in the stereoregular catalyst (A) is from 0.0l to l.0; and the second polymerization being carried out in one or more reaction vessels using an ethylene/propylene feed containing from l0 to l00% by weight of ethylene, based on the total weight of ethylene and propylene, to produce from 5 to 40% by weight of the final polymerization product.