A mathematical theory of dense spray flows is described. It is based on treating the flow both inside and outside the drops via the incompressible Navier-Stokes equations and the interface as Gibb＇s dividing surface. Taking into account the information necessary to describe the dynamical state of the flow, a hyperspace is constructed which describes the state of the system at any instant. This hyperspace consists of a number of field axes- one which describes the instantaneous velocity field and a number which describes the instantaneous morphology of the fluids. Following the methods if statistical mechanics, an ensemble of microscopically identical flows is used to define a density of system points in the hyperspace. A transport equation is then written which describes the evolution of those collection of flows for all time. A unique features of this transport equation is that the dynamics of each fluid element are embedded in the transport equation- that is, the Navier-Stokes equations and interface jump conditions are implicit constraints on the overall transport of a system point in hyperspace. The utility of the resulting equation (the continuum-particle, continuum-field equation) is demonstrated by shoeing that it can be reduced, in the limit of small dispersed-phase elements, to the point-particle, continuum-field equation which. in turn, has been shown to reduce to the ensemble-averaged Navier-Stokes and spray equations. As such, the present development is the uppermost level of a hierarchy of models of continuum treatment of spray flows- analogous to the Liouville equation of the kinetic theory of gases.