We investigate feedback control solutions to the slugging problem occuring on oil wells and flowlines. This gas-liquid flow instability, characterized by large oscillations of the pressures and flow rates inside the transport pipes, causes production losses and may damage the facilities. Using pressure sensors in feedback loops, the flow can be stabilized using the outlet valve as the actuator. Both finite and infinite dimensional models allow us to build observers and design control laws better suited to this underactuated system than the PI controllers commonly used in this industry.