Controlled pressure drilling of a borehole with a drilling system detects events and identifies the events as being one of a gas-at-surface event, a kick event, a high-pressure low-volume depletion event, and a gas expansion event. Parameters including flow-in, flow-out, density, and standpipe pressure are monitored. A volume increase is detected between the flow-in and flow-out, and an initiation point of the detected volume increase is identified. At this point, an event from the initiation point is identified based on the monitored parameters from the initiation point. To identify a kick event, for example, the standpipe pressure is determined to have increased from the initiation point without the density decreasing since the initiation point, and a cumulative volume value from the initiation point is determined to be above a first threshold. In response to the identified event, an action is initiated in the drilling system.