A process for the preparation of propylene homopolymers or copolymers by polymerizing the monomer or monomers in the gas phase in a centric stirred bed of finely divided polymer, with removal of the heat of polymerization by evaporative cooling, the temperature in the polymerization zone being regulated by measuring the temperature continuously and causing any change therein to trigger a change in the amount of liquid monomer, evaporating in the reaction zone, which is introduced per unit time, in which process(1) the radius and height of the centric stirred bed are in a particular ratio to one another, (2) the finely divided polymer in the centric stirred bed is caused to move upward in the peripheral zone of the bed and downward in the central zone of the bed, (3) the temperature in the polymerization zone is regulated by simultaneously measuring it at (3.1) one or more points of the inner part of the stirred bed and (3.2) one or more points of the outer part of the stirred bed and (4) the actual temperatures T determined simultaneously at the individual points of measurement are combined to give a temperature parameter T.sub.M and the difference of this parameter from the intended value triggers the regulating sequence, or the temperature differences .DELTA.T between the actual and intended temperatures, measured simultaneously at the individual points of measurement, are combined to give a difference parameter .DELTA.T.sub.M and this parameter triggers the regulating operation.