A process for the manufacture of a linear polyethylene with narrow molecular-weight distribution comprising polymerizing ethylene alone or a mixture of ethylene and an alpha-olefin in which ethylene represents at least about 70% by weight of the total monomers involved, in a gas-phase polymerization medium in the presence of a catalytic component containing at least one transition metal, magnesium, and a halogen, a co-catalyst comprising an alkylaluminum compound, and a monoether, the monoether having the general formula R'OR", wherein R' and R" are the same or different and each is a C.sub.1 to C.sub.8 linear or branched hydrocarbon radical or being a cyclic monoether with the oxygen forming a ring having 4 to 12 carbon atoms.