A subsea multiphase fluid separator having a gas separator 22 for separating gas from a wellstream containing oil. A water separation stage 24 is provided downstream of the gas separator, having at least one dual pipe separator 24 for separating water from the oil of the wellstream. A water treatment system 54 is also provided for cleaning oil from water that is produced by the water separation stage. Optionally, the water separation stage has an electrocoalescer 108 and at least one second separator 112 in series, downstream of the or each dual pipe separator on an oil outlet path. Optionally, there is water-in-oil sensor 116 downstream of the water separation stage or an oil-in-water sensor 114 downstream of the water treatment system. Optionally, water treatment system has at least one flotation unit having a water inlet for water to be cleaned of oil; a water outlet for water cleaned of oil; and a reject outlet for gas mixed with oil cleaned from the water. The inlet of the or each flotation unit can comm
