A system for separating fluids from a hydrocarbon well production fluid mixture at a subsea location has a centrifugal separator (16) for separating the mixture into gas and liquid. A hydrocyclone separator (32) then separates the liquid into oil and water and an oil-in-water sensor (38) detects the amount of oil in water leaving the separator. If the sensor (38) detects that the water contains more than the prescribed amount of oil, the water is recirculated through the hydrocarbon separator (32) for removal of further oil form water. The hydrocyclone separator (32) has a level interface sensor (66) and if this sensor detects that the oil/water interface is not within prescribed limits for optimum separation of the oil and water, the amount of oil removed from the separator is adjusted until the oil/water interface is within the prescribed limits. The sensors (38, 66) are connected to a control means (68) which controls electrically actuable control valves (42, 58) to cause the water to be recirculated to adjust the amount of oil removed from the hydrocarbon separator. The system also includes a gas slug detection device (14) upstream of the centrifugal separator (16) for sensing the presence of a gas slug in the production fluid. A liquid flow control valve (21) is adjusted by the control means (68) to ensure that the level of liquid in the centrifugal separator (16) does not fall below prescribed limits.