Through a combination of bulk, interface, and interphase effects, water-in-salt electrolytes, employing a high salt concentration, offer a wider electrochemical stability window than traditional dilute aqueous electrolytes. Here we explore chemical stability, conductivity, viscosity, and electrochemical stability of aqueous solutions of bis(fluorosulfonyl)imide (FSI) salts as electrolytes for lithium-ion and sodium-ion batteries. We demonstrate that the FSI anion is prone to hydrolysis in this environment. However, the kinetics of the reaction strongly depend on salt concentration and nature of the cation. Interestingly, we find that NaFSI solutions are significantly more stable than LiFSI solutions. Highly-concentrated NaFSI solutions also display a wide electrochemical stability window and high conductivity.