Abstract: Polyolefins, preferably polyethylene, are prepared in a continuous gas-phase polymerization process in which the fluid monomeric component, preferably ethylene, and, optionally, one or more comonomers is/are polymerized in the polymerization zone of a fluidized-bed reactor in the presence of one or more catalysts, optionally with the addition of various auxiliaries, under reaction conditions where the fluidizing gas is circulated to remove the heat of polymerization or reaction and the polymerization product is taken from the circuit and the corresponding amount of monomer and, optionally, comonomers and optionally further auxiliaries are fed in, wherein the fluidizing gas discharged from the fluidized-bed reactor is cooled by means of a direct cooling apparatus in which the coolant is brought into direct contact with the fluidizing gas and heated coolant is passed to at least one further cooling stage in order to cool it and is, after cooling, wholly or partly returned to the direct cooling apparatus and/or