A method of identifying a self-sustained influx of formation fluids into a wellbore includes the steps of closing an annular shut-off device and diverting an annular return flow from the wellbore through a first flow rate measurement device, measuring a flow rate of said annular return flow, measuring an inlet flow rate of fluids entering the well through a second flow rate measurement device in a fluid injection line, and identifying a self-sustained influx of formation fluids if a non-decreasing measured annular return flow rate is greater than said measured inlet flow rate.