A method and equipment for reducing or avoiding multiple dispersions in fluid flows each having two or more non-mixable fluid components with different specific gravities and viscosities, in particular fluid flows of oil, gas and water from different oil/gas production wells (B1-B8) in formations beneath the surface of the earth or sea. The fluid flow from each well (B1-B8), depending on whether it is oil-continuous (o/w) or water-continuous (w/o), is fed to a transport pipeline (T) so that the oil-continuous fluid flows (o/w) are supplied to the transport line (T) first and the water-continuous fluid flows (w/o) second, or the two fluid flows (o/w, w/o) are fed to two separate transport lines (T1, T2). In a preferred embodiment, the two separate transport lines (T1, T2) may be connected to a common transport line (T); the two fluid flows (o/w, w/o) are mixed before further transport and any subsequent separation in a separator. In another preferred embodiment, each of the fluid flows in the respective transport lines (T1, T2) may be fed to a common separator (H) or its own independent separator.