A process and apparatus for continuous treatment of suspensions which include solid matter difficult to decant such as solid matter tending to plasticize under temperature and/or pressure loads, solid matter having a rheopexy behavior, and solid matter having at least one of high water absorption and low specific gravity differences with respect to the liquid of the suspension. The apparatus includes a solid-shell screw-conveyor centrifuge system having a rotatable screw and rotatable shell with one of the screw and shell being driven by a drive mechanism and the other of the shell and screw being joined by a hydraulic motor. A control system is provided for controlling at least one of the differential speed between the screw and shell and the speed of the shell in dependence upon the nature of the suspension being processed.