Gas-liquid mixtures, such as produced from crude oil reservoirs, are separated in a separator system having a separator vessel with a spiral inlet duct for centrifuging the gas-liquid mixture and an active centrifuge for removing entrained gas after primary separation by the spiral inlet duct. Active centrifuging is carried out by a rotating member disposed in a second compartment in the separator vessel having a plurality of circumferentially-spaced, radially-extending chambers for imposing centrifugal force on a quantity of liquid in each chamber. The chambers may discharge liquid through a porous outer cylindrical wall or through axially disposed discharge ports. The plural chambers minimize remixing of gas and liquid during centrifuging. The centrifuge may be an external rotary-tube type centrifuge with plural separator chambers. The centrifuge may also include a pump connected to the separator liquid discharge line for reintroducing a portion of the liquid into a secondary space in the separator vessel in a centrifugal flow path to further force gas-liquid separation through centrifugal forces acting on the mixture.