A self-propelled or stationary construction machine or agricultural machine is provided having a rotatable work device, in particular, a work device for processing soil surfaces or for chopping material. The machine has a drive device for the work device, the drive device having a first drive source and a switchable coupling unit between the first drive source and the work device for engaging the work device with the first drive source. The drive device is equipped with an additional drive unit, the machine being configured for controlling the drive device to accelerate the work device by means of the additional drive unit to an operating speed which would result during operation of the work device by means of the first drive source. In addition, an associated method for driving a work device of a construction or agricultural machine is disclosed.