A device and process generates an alarm during a machine-assisted ventilation of a patient. A minute volume is measured and a median of the minute volume and a lower critical limit value of the minute volume and a time delay are determined and are recorded in a control device. A reference signal is determined as a function of the lower critical limit value for the minute volume and the time delay based on the median of the minute volume. From the reference signal an alarm limit value located below the lower critical limit value as well as a value for a maximum tolerated duration of apnea of the patient are derivable. An alarm signal is generated both during an undershooting of the lower critical limit value over a period of time that is longer than the established time delay and during an undershooting of the alarm limit value.