Process for preparing a copolymer of ethylene and a 1,3-diene of formula which comprises ethylene units and units of the 1,3-diene, the ethylene units in the copolymer representing between 50 mol% and 95 mol% of the ethylene units and of the units of the 1,3-diene present in the copolymer, the units of the 1,3-diene of 1,2 and 3,4 configuration in the copolymer representing more than 50 mol% of the units of the 1,3-diene present in the copolymer, which process comprises the polymerization of ethylene and 1,3-diene in a reactor in the presence of a catalytic system based on at least one metallocene of formula and an organomagnesium compound of formula CH 2 =CR-CH=CH 2 P(Cp 1 Cp 2)Nd(BH 4) (1+y) -L y -N x MgR 1 R 2 the symbol R representing a hydrocarbon chain having from 3 to 20 carbon atoms, Cp 1 and Cp 2, which are identical or different, being selected from the group consisting of substituted fluorenyl groups and the unsubstituted fluorenyl group of formula C 13 H 8, P being a group bridging the two Cp 1 and Cp 2 groups and representing a ZR 3 R 4 group, Z representing a silicon or carbon atom, R 3 and R 4, which are identical or different, each representing an alkyl group comprising from 1 to 20 carbon atoms, preferably a methyl, y, which is an integer, being equal to or greater than 0, x, which is or is not an integer, being equal to or greater than 0, L representing an alkali metal selected from the group consisting of lithium, sodium and potassium, N representing a molecule of an ether, preferably diethyl ether or tetrahydrofuran, R 1 and R 2, which are identical or different, representing a carbon group, ethylene and 1,3-diene being added continuously to the reactor during the polymerization. the ethylene units in the copolymer representing between 50 mol% and 95 mol% of the ethylene units and of the units of the 1,3-diene present in the copolymer, the units of the 1,3-diene of 1,2 and 3,4 configuration in the copolymer representing more than 50 mol% of the units of the 1,3-diene present in the copolymer, which process comprises the polymerization of ethylene and 1,3-diene in a reactor in the presence of a catalytic system based on at least one metallocene of formula and an organomagnesium compound of formula CH 2 =CR-CH=CH 2 P(Cp 1 Cp 2)Nd(BH 4) (1+y) -L y -N x MgR 1 R 2 the symbol R representing a hydrocarbon chain having from 3 to 20 carbon atoms, Cp 1 and Cp 2, which are identical or different, being selected from the group consisting of substituted fluorenyl groups and the unsubstituted fluorenyl group of formula C 13 H 8, P being a group bridging the two Cp 1 and Cp 2 groups and representing a ZR 3 R 4 group, Z representing a silicon or carbon atom, R 3 and R 4, which are identical or different, each representing an alkyl group comprising from 1 to 20 carbon atoms, preferably a methyl, y, which is an integer, being equal to or greater than 0, x, which is or is not an integer, being equal to or greater than 0, L representing an alkali metal selected from the group consisting of lithium, sodium and potassium, N representing a molecule of an ether, preferably diethyl ether or tetrahydrofuran, R 1 and R 2, which are identical or different, representing a carbon group, the symbol R representing a hydrocarbon chain having from 3 to 20 carbon atoms, Cp 1 and Cp 2, which are identical or different, being selected from the group consisting of substituted fluorenyl groups and the unsubstituted fluorenyl group of formula C 13 H 8, P being a group bridging the two Cp 1 and Cp 2 groups and representing a ZR 3 R 4 group, Z representing a silicon or carbon atom, R 3 and R 4, which are identical or different, each representing an alkyl group comprising from 1 to 20 carbon atoms, preferably a methyl, y, which is an integer, being equal to or greater than 0, x, which is or is not an integer, being equal to or greater than 0, L representing an alkali metal selected from the group consisting of lithium, sodium and potassium, N representing a molecule of an ether, preferably diethyl ether or tetrahydrofuran, R 1 and R 2, which are identical or different, representing a carbon group, ethylene and 1,3-diene being added continuously to the reactor during the polymerization.