Water-in-salt electrolytes have attracted considerable interest in the past decade for advanced lithium-ion batteries, possessing important advantages over the non-aqueous electrolytes currently in use. A battery with a LiTFSI-water electrolyte was demonstrated in which an operating window of 3 V is made possible by a solid-electrolyte interface. Viscosity is an important property for such electrolytes, because high viscosity is normally associated with low ionic conductivity. Here, we investigate shear and longitudinal viscosities using shear stress and compressional longitudinal stress measurements as functions of frequency and concentration. We find that both viscosities are frequency-dependent and exhibit almost identical frequency and concentration dependences in the high-concentration region. A comparison to quasielastic neutron scattering experiments suggests that both are governed by structural relaxation of the TFSI- network. Thus, LiFTSI-water electrolytes appear to be an unusual case of a non-Newtonian fluid, where shear and longitudinal viscosities are determined by the same relaxation mechanism.