Fullerenols C-60(OH)(X) and C-70(OH)(X) (X similar to 30) have been studied in aqueous solutions at the concentrations 0.05-22wt% by X-ray and neutron scattering and using modeling hydroxyls' arrangements on carbon cages to explain the molecular assembly defined by hydrophobic and hydrophilic interactions of molecules. In the case of C-60 quantum chemical calculations minimizing molecular energy for different configurations of OH-groups on the carbon cages showed their preferred localization at C-60 spheroids' equatorial zone and at the opposite poles. However, less symmetric hydroxyls' localization on C-70 molecules was found since hydroxyls do not create closed chains on them. As a result, the molecules C-60(OH)(X) are associated into primary chain-like aggregates (similar to 20 units, few nanometers in size) more likely in water than the fullerenols C-70(OH)(X) forming similar groups of lower aggregation degree. For C-60(OH)(X) and C-70(OH)(X) the peculiarities in hydroxyls' grafting affected a coordination of primary groups integrated into secondary and tertiary structures at the distances R similar to 5 nm and R similar to 30 nm at the concentrations C > 5wt% and C > 10wt%, respectively. The discovered mechanism of fullerenols' assembly in water will facilitate their use in chemistry and biomedicine.