An automated system for detecting fluid influx into a wellbore during the transient conditions that occur after pumps stopped. The system comprises at least one sensor normally employed on a drilling rig for measuring at least one parameter, and a processor for receiving a signal indicative of the parameter from the sensor. The processor is programmed to analyze a plurality of values of the parameter measured during a plurality of previous events so as to generate a predetermined threshold value, compare the received signal to the predetermined threshold value, and provide an output signal indicative of fluid influx when the received signal is beyond the predetermined threshold value.