The talk is devoted to the measure-valued processes describing the random transformation of the measure related to the motion on the phase space. This motion is considered in the terms of the stochastic flows on the initial space.In connection with this the new kind of the stochastic differential equation for the stochastic flows with interaction is considered. The solutions to these equations are not the single trajectories but the flows on the whole space. In the talk the existence of different types of solutions and its behavior on infinity are considered. The local times and the structure of the additive functional for the corresponding class of Markov measure-valued processes also are described.