Abstract: Propylene polymers which comprise from 25 to 97% by weight of a propylene polymer (I) containing from 0 to 15% by weight of copolymerized C.sub.2 -C.sub.10 -alk-1-enes and also comprise from 3 to 75% by weight of a further propylene polymer (II) containing from 15 to 80% by weight of copolymerized C.sub.2 -C.sub.10 -alk-1-enes, are obtainable by two-stage polymerization of propylene and C.sub.2 -C.sub.10 -alk-1-enes in the presence of a Ziegler-Natta catalyst system which comprises a titanium-containing solid component a) comprising a compound of magnesium, a halogen, silica gel as support and a carboxylic ester as electron donor compound, and also as cocatalysts an aluminum compound b) and a further electron donor compound c), where, in a first polymerization stage, propylene is polymerized in the presence or absence of further C.sub.2 -C.sub.10 -alk-1-enes at from 50.degree. to 100.degree. C., pressures in the range from 15 to 40 bar and a mean residence time of from 0.

Abstract: Multiphase block copolymers of propylene comprisinga) a polymer of propylene with from 0 to 5% by weight of further C.sub.2 -C.sub.10 1-alkenes,b) a copolymer of propylene with from 5 to 98% by weight of further C.sub.2 -C.sub.10 1-alkenes,the multiphase block copolymers having a melting point of less than 155.degree. C. and a stiffness (shear modulus G) conforming to the following condition (I): ##EQU1## where M.sub.a) denotes the amount of propylene polymer a) and M.sub.co denotes the amount of the multiphase block copolymer.are obtainable in particular by polymerization by means of metallocene-containing catalyst systems.

Abstract: Random propylene copolymers containing copolymerized C.sub.2 -C.sub.10 -alk-1-enes are obtainable by polymerization of propylene and C.sub.2 -C.sub.10 -alk-1-enes in the presence of a Ziegler-Natta catalyst system comprising a titanium-containing solid component a) comprising a compound of magnesium, a halogen, silica gel as support and a carboxylic ester as electron donor compound, and also, as cocatalysts, an aluminum compound b) and a further electron donor compound c), where propylene and the C.sub.2 -C.sub.10 -alk-1-enes are polymerized with one another at from 50.degree. to 100.degree. C. at pressures in the range from 15 to 40 bar and mean residence times of from 0.5 to 5 hours and the support used in the titanium-containing solid component is a silica gel which has a mean particle diameter of from 5 to 200 .mu.m, a mean particle diameter of the primary particles of from 1 to 10 .mu.m and voids or channels having a mean diameter of from 1 to 10 .mu.

Abstract: Highly flexible propylene/ethylene copolymers having a high rubber content are obtainable by two-stage polymerization from the gas phase in an agitated fixed bed by means of a Ziegler-Natta catalyst system which, in addition to a titanium-containing solid component, also contains an aluminum compound as a cocatalyst, in a first polymerization stage, propylene being polymerized at from 15 to 40 bar and from 50.degree. to 90.degree. C. and during an average residence time of the reaction mixture of from 0.5 to 5 hours and then, in a second polymerization stage, a mixture of propylene and ethylene being polymerized with the polymer discharged from the first polymerization stage, at from 5 to 30 bar, this pressure being at least 2 bar below the pressure of the first polymerization stage, and at from 60.degree. to 100.degree. C. and during an average residence time of the reaction mixture of from 0.

Abstract: Metallocene catalyst systems for the polymerization of C.sub.2 -C.sub.10 -alkenes are obtainable by deactivation of a preactivated metallocene catalyst system which contains, as active components, a metallocene complex of a metal of subgroup IV or V of the Periodic Table and an oligomeric alumoxane compound and, if required, subsequent reactivation.

Abstract: Propylene-ethylene copolymers are obtained by two-stage polymerization from the gaseous phase in an agitated fixed bed by means of a Ziegler-Natta catalyst system that contains in addition to a titanium-containing solid component also an aluminum compound as co-catalyst, wherein as Ziegler-Natta catalyst system a system is used which, following the reaction of the titanium-containing solid component with the co-catalyst, is deactivated by reaction with carbon dioxide. The copolymers are used for producing fibers, films and moldings.