Process for the preparation of a composition containing ethylene polymers comprising a polymer of melt index MI.sub.2 of 5 to 1000 g/10 min and a polymer of melt index MI.sub.5 of 0.01 to 2 g/10 min, the ratio of these indices being from 500 to 50,000 and the weight ratio of the two polymers being equal to (30 to 70):(70 to 30), according to which part of the ethylene, a catalyst derived from a transition metal having an intrinsic molecular weight distribution defined by an intrinsic M.sub.w /M.sub.n ratio less than or equal to 10 and a deactivation constant less than or equal to 0.5 h.sup.-1, and a cocatalyst are introduced into a first reactor, polymerization of the ethylene is carried out therein, a mixture comprising one of the polymers, the catalyst and the cocatalyst is drawn off from this reactor and the mixture and another part of the ethylene are introduced into a second reactor, which ethylene is polymerized to form the other polymer.

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