A process for the polymerisation of olefins is described involving the use of a catalyst system comprising a supported transition metal compound and an activator based on an organoborane and an aluminoxane. Preferably the transition metal compound is a metallocene complex. The support is pretreated with an organoaluminium compound and the process is particularly suitable for the gas phase preparation of copolymers of ethylene and alpha-olefins having a molecular weight distribution in the range 2.5-7.0 and a melt strength in the range 3-12 cN.