We have investigated water highly diluted in 1-alkyl-3-methyl imidazolium ionic liquids (ILs) with hexafluorophosphate {PF6-} and tetrafluoroborate {BF4-} anions using vibrational spectroscopic measurements in tile nu(OH) spectral domain of water (3600-3800 cm(-1)) and DFT calculations. The measured profiles exhibit two well-defined bands at coinciding vibrational transitions assigned with the nu(1) symmetric and nu(3) antisymmetric OH stretching modes of monodispersed water. The local organization and the vibrational spectra of water diluted in ILs have been assessed by DFT calculations (using the B3LYP functional and 6-31+G** basis set). We show that the predicted structures of water interacting (minimally) with two anions in nearly "symmetric" structures of type (A center dot center dot center dot H-O-H center dot center dot center dot A) lead to spectral features consistent with the previous spectroscopic observations as well as with those reported here. We emphasize the role of the non additive interaction forces (especially the 3-bodies electrostatic interactions) in the structural organization taking place between the cation-anion Couples and for determining preferentially (A center dot center dot center dot H-O-H center dot center dot center dot A) associations of water with the anions as well as their consequences on tile vibrational spectra of water. We show that the doubly hydrogen-bonded character of water in such associations leads to well-defined spectral features, which are the shifts of the nu(1) and nu(3) stretching modes of water, the separation Delta nu(13) between them (about 80 cm (1)), and the intensity ratio estimates R = I nu(3)/I nu(1) (IR absorption and Raman). Finally, we evoke the fact that the H-bond interactions of water diluted in these ILs involve a more noticeable electrostatic character than for H-bond interactions of water in usual molecular solvents. In this context, we emphasize that the appearance of the Raman band of the nu(3) mode of water originates from a significant polarization of water due to the local electrostatic fields induced by surrounding ions.