Abstract: A method and apparatus for controlling the riser base pressure and detecting well control problems, such as kicks or lost circulation, during drilling of an offshore well using a gas-lifted riser. The pressure control apparatus preferably includes two separate control elements, one to adjust the pressure at the surface (prs) and the mass flow rate out of the top of the riser ({dot over (m)}o) to compensate for changes in riser base pressure (prb) and the other to adjust either or both of the boost mud flow rate (qb) and lift gas flow rate (qg) to maintain a constant or nearly constant mass flow rate entering the base of the riser ({dot over (m)}i). According to the method of the present invention, the well return flow rate (qw) is preferably determined by directly measuring various other parameters and then computing qw from the measured parameters. The computed value of qw may be compared to the drill string flow rate (qc) to detect well control problems, such as kicks or lost circulation.