Process for the transition between an ethylene co-polymerization process in a polymerization reactor in the presence of a catalyst and of ethylene E and an olefin co-monomer A to produce an ethylene copolymer PEA into an ethylene co-polymerization process carried out in the same polymerization reactor in the presence of a catalyst and of ethylene E and an olefin co-monomer B to produce an ethylene copolymer PEB. Co-monomers A and B are different and are both present in the reactor during at least part of the transition from PEA to PEB. The transition is performed continuously by (i) starting the transition by stopping steady state production of ethylene copolymer PEA and (ii) ending the transition when steady state production of ethylene copolymer PEB is achieved.