The invention concerns a method for producing ethylene homopolymers or copolymers comprising at least 90 mol % of units derived from ethylene which consists in: contacting in polymerising conditions, the monomers with a catalytic system including: (a) a catalytic solid comprising a metallocene of a transition metal of groups 4 to 6 of the periodic table containing at least a cyclopentadiene ligand capable of being substituted and a support, (b) at least an organoaluminium compound selected among compounds of general formula (1): AlTx(Y′)yX′z wherein: T is a hydrocarbon group containing 1 to 30 carbon atoms; Y′ is a group selected among —OR′, —SR′ and NR′R″ with R′ and R″ independently representing a hydrocarbon group containing 1 to 30 carbons atoms; X′ is a halogen atom: x verifies the relationship 0