A process for the manufacture of olefin polymers by polymerizing .alpha.-monoolefins at relatively low temperatures and relatively low olefin pressures by means of a catalyst obtained from a silicate carrier (component a), an aluminum compound (component b) and a chromium compound (component c). The catalyst is obtained by (1) in a first stage, initially (1.1) charging a particular silicate carrier (component a) with (1.2) a mixture of (1.2.1) an aluminum salt or a mixture of an aluminum salt with up to 80 mole%, based on the salt mixture, of a nickel-II salt (component b) and (1.2.2) a chromium compound (component c), this compound being chromium trioxide or a compound which is converted to chromium trioxide under the conditions of stage (2), by treatment with a solution of the mixture (1.2), and (2), in a second stage then maintaining the product, obtained from stage (1), for a certain time at a high temperature in an anhydrous oxygen-containing gas stream. The process may be used to produce polymers having a relatively broad molecular weight distribution.