"Water-in-salt" (WIS) and "water-in-bisalt" (WIBS) electrolytes have recently been developed for Li-ion batteries, combining the safety and environmental friendliness of aqueous electrolytes with a larger operating window made possible by a solid-electrolyte interphase. We report quasielastic neutron scattering (QENS) measurements on solutions of a WIS electrolyte at two concentrations, 13.9 and 21 m (molal) lithium bis(trifluoromethane)sulfonimide LiTFSI in H2O/D2O and a WIBS electrolyte at (21 m LiTFSI + 7 m lithium triflate (LiOTf)) in H2O/D2O. The data were Fourier transformed to obtain experimental intermediate scattering functions (ISFs) and compared with corresponding quantities obtained from molecular dynamics (MD) simulations. Both QENS and MD ISFs could be fitted well by a single stretched exponential function to obtain apparent translational diffusion coefficients for the water molecules. The QENS values agree well with the MD simulations for the 13.9 and 21 m solutions, but MD simulations predict a slower relaxation of water compared to QENS for the WIBS electrolyte. Comparison of the incoherent and coherent scattering reveals much faster water dynamics compared with structural relaxation of the ionic framework, consistent with the nanodomain picture where the lithium diffusion occurs through the tortuous water domain around the slower relaxing ionic matrix, leading to highly non-Gaussian water motion.