The time-, space- and time-space-averaged bulk transport equations for multiphase flow systems are derived through a systematic averaging procedure based on a suitable definition for phase indicator functions with a single scalar argument. Then the local instantaneous field equations, used as a starting point, are integrated in the appropriate multidimensional fields, in a way analogous to the one used for a one-dimensional field. Also the time-, space- and time-space-averaged expressions for the main geometric parameters of the multiphase systems, holdup and specific interfacial area, are consistently developed for each averaging type.