The invention relates to a process for the production of ethylene polymers by the polymerization of ethylene or the copolymerization of ethylene with one or more C.sub.3 to C.sub.8 olefins in contact with a chromium-based catalyst deposited on a support essentially consisting of silica. According to the invention, the chromium catalyst is subjected in succession to a heat treatment in nitrogen and then to a heat treatment in air under defined temperature conditions before bringing it into contact with ethylene and, optionally, one or more olefins under polymerizing conditions. The process of the invention makes it possible to manufacture ethylene polymers having an improved compromise between processability, stiffness and resistance to slow crack growth.