A mixture of fluids is separated into at least two phases, one of which has a higher density than the other, passing the mixture through a normally horizontal supply pipe, by creating a stratified flow in the supply pipe, by passing the mixture through an inclined pipe, whilse maintaining a stratified flow in the inclined pipe, by extracting fluid with lower density ("lighter phase") via a first discharge system and fluid with a higher density ("heavier phase") via a second discharge system, wherein the interface between the lighter phase and the heavier phase is monitored in the inclined pipe by a level controller means that varies the flow of the fluid of higher density to keep the interface between set levels.