A ventilating system for supplying a patient with respiratory gas has an apparatus for measuring a respiratory gas flow curve 27 and a respiratory gas pressure curve 28 and has an evaluation circuit 8 for processing at least the respiratory gas flow curve and switching over the respiratory phases. As switchover values from one respiratory phase to the other, the evaluation circuit 8 utilizes predetermined trigger thresholds T.sub.IL, T.sub.EL of the respiratory gas flow curve 27. The ventilating system is improved in such a manner that a good adaptation thereof to the breathing effort of the patient 2 is provided even when leakage is present. This task is solved in that, in the evaluation circuit, the respiratory gas flow curve 27 and the respiratory gas pressure curve 28 are logically coupled during both the inspiratory phase and the expiratory phase. This logic operation takes place in accordance with a predetermined function. From the foregoing, an inspiratory trigger ancillary threshold Z.sub.I and an expiratory trigger ancillary threshold Z.sub.E are computed as an additional switchover criterion. These trigger ancillary thresholds Z.sub.I and Z.sub.E are added to the trigger thresholds T.sub.IL and T.sub.EL, respectively. A method for triggering the respiratory phase in the system is also disclosed.