A method of operating a system for handling an influx of gas into a marine riser during the drilling of a well bore includes the steps of operating a first riser closure apparatus to close the riser at a first point above a flow spool provided in the riser, there being a riser gas handling line extending from the riser at the flow spool to a riser gas handling manifold, operating a second riser closure apparatus to close the riser at a second point below the flow spool, pumping fluid into an inlet line which extends into the riser at a point above the second point but below the flow spool, and operating a choke provided in the riser gas handling manifold to maintain the pressure in the inlet line or the riser at a substantially constant pressure.