Crystalline polymers and copolymers of propylene having total MIL values>2 g/10 minutes, total [η] values in tetrahydronaphthalene at 135° C.≦2.8 dl/g, Mw/Mn values>20, a fraction insoluble in xylene at 25° C.≧94, and including from 10 to 60% by weight of a fraction (A) having [η]≧2.6, are prepared by way of sequential polymerization in at least two stages, in the presence of a particular Ziegler-Natta catalysts supported on magnesium halides. These polymers have high melt strength, high mechanical properties, and are particularly adequate for the manufacture of articles by using various conversion technologies, such as for example extrusion in thin sheets to be subjected to thermoforming, as well as for injection molding, and blow molding.