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One of the major claims against homeopathy is that ultra-high dilutions (UHD) of biologically active substances are identical to a pure solvent used and therefore cannot possess biological activity. Thus, it is necessary to find out if UHD differ from the solvent in their physical-chemical properties. Recently revolutionary discoveries concerning the properties of aqueous systems with “normal” concentrations of solutes as well as of UHD prepared from them were made. Contrary to the current opinion that solutions are homogenous systems it turned out that sub-micrometer “domains” consisting of both solute and solvent molecules emerge after dissolution solutes in water. Upon dilution even to ultra-high degrees sub-micrometer structures do not disappear; on the contrary their size usually grows up. These structures in UHD called "nanoassociates" (NA) by A.I. Konovalov are negatively charged; their charge and sizes change nonmonotonically with serial dilutions. Patterns of NA parameters correlate with biological effects produced by UHD. Shielding of UHD from ambient electromagnetic fields (EMF) prevents NA emergence in UHD; paradoxical properties differentiating them from pure water including biological activity also disappear. Therefore, aqueous systems containing domains and NA (in non-shielded from EMF UHD) should be considered disperse systems rather than classical solutions. Emergence of domains and NA in them represents the process of self-organization turning them into dissipative non-equilibrium entities. Dynamic structuring of aqueous disperse systems with charge separation in them is provided by energy supplied by environmental EMF and redox reactions with the participation of reactive oxygen species permanently proceeding in aqueous systems. We suppose that newly discovered properties of UHD representing disperse systems of a "water in water" kind prove that they are basically different from a pure solvent, suggesting that homeopathy has a scientific foundation.