The self-propelled construction machine according to the invention, in particular road-milling machine, recycler, stabiliser or surface miner, comprises a machine frame 2, which is supported by a chassis 1, which has wheels or tracks 1A, 1B. A milling drum 4 is arranged on the machine frame. The wheels or tracks 1A, 1B and the milling drum 4 are driven by a drive unit 8. Furthermore, the construction machine comprises a control unit 19 for controlling the drive unit 8 and a signal-receiving unit 18 for detecting at least one measurement variable M(t) which is characteristic of an operating state of the milling drum 4. The construction machine is characterised in that the rotational speed of the milling drum 4 is adapted, on the basis of at least one measurement variable M(t) which is characteristic of a critical operating state of the milling drum, to the operating conditions of the construction machine in such a way that the milling drum is operated in a non-critical operating state. The adaptive open-loop control of the milling drum rotational speed allows the construction machine to be operated at an optimum operating point with respect to the milling drum rotational speed.