A ventilator machine having: a source of gas for breathing; a ventilator unit arranged to feed gas for breathing through connecting lines; a control unit arranged to control the ventilator unit; sensors arranged to pick up at least one pneumatic signal for breathing activity which are connected to the control unit; the control unit being arranged to: control the ventilator unit of the ventilator machine to have successive changeovers between two phases of ventilation, the two phases being inspiration and expiration, by examining, in one phase of ventilation, a sensed signal for breathing activity for a threshold criterion for a changeover to the next phase of ventilation and changing the ventilator machine over from one phase of ventilation to the other when the threshold criterion is met; and control the ventilator unit of the ventilator machine at the changeover to the new phase of ventilation in such a way that a pneumatic ventilation parameter, selected from airway pressure and flow, is moved from an actual value to a target value for the new phase of ventilation which is set in advance; the ventilator machine being characterised in that the control unit is also arranged to: divide the change in the breathing parameter from the actual value to the target value into a plurality of part-stages at the changeover of the phase of ventilation and, after each part-stage, to again examine the current signal for breathing activity for the threshold criterion responsible for the triggering of the current changeover and, if this threshold criterion is no longer met, to jump back automatically to the state of operation of the ventilator machine before the last changeover, or otherwise to continue to the next part-stage. a source of gas for breathing; a ventilator unit arranged to feed gas for breathing through connecting lines; a control unit arranged to control the ventilator unit; sensors arranged to pick up at least one pneumatic signal for breathing activity which are connected to the control unit; the control unit being arranged to: control the ventilator unit of the ventilator machine to have successive changeovers between two phases of ventilation, the two phases being inspiration and expiration, by examining, in one phase of ventilation, a sensed signal for breathing activity for a threshold criterion for a changeover to the next phase of ventilation and changing the ventilator machine over from one phase of ventilation to the other when the threshold criterion is met; and control the ventilator unit of the ventilator machine at the changeover to the new phase of ventilation in such a way that a pneumatic ventilation parameter, selected from airway pressure and flow, is moved from an actual value to a target value for the new phase of ventilation which is set in advance; the ventilator machine being characterised in that the control unit is also arranged to: divide the change in the breathing parameter from the actual value to the target value into a plurality of part-stages at the changeover of the phase of ventilation and, after each part-stage, to again examine the current signal for breathing activity for the threshold criterion responsible for the triggering of the current changeover and, if this threshold criterion is no longer met, to jump back automatically to the state of operation of the ventilator machine before the last changeover, or otherwise to continue to the next part-stage. control the ventilator unit of the ventilator machine to have successive changeovers between two phases of ventilation, the two phases being inspiration and expiration, by examining, in one phase of ventilation, a sensed signal for breathing activity for a threshold criterion for a changeover to the next phase of ventilation and changing the ventilator machine over from one phase of ventilation to the other when the threshold criterion is met; and control the ventilator unit of the ventilator machine at the changeover to the new phase of ventilation in such a way that a pneumatic ventilation parameter, selected from airway pressure and flow, is moved from an actual value to a target value for the new phase of ventilation which is set in advance; the ventilator machine being characterised in that the control unit is also arranged to: divide the change in the breathing parameter from the actual value to the target value into a plurality of part-stages at the changeover of the phase of ventilation and, after each part-stage, to again examine the current signal for breathing activity for the threshold criterion responsible for the triggering of the current changeover and, if this threshold criterion is no longer met, to jump back automatically to the state of operation of the ventilator machine before the last changeover, or otherwise to continue to the next part-stage.