Aqueous Li/Air secondary battery cells are configurable to achieve high energy density and prolonged cycle life. The cells include a protected a lithium metal or alloy anode and an aqueous catholyte in a cathode compartment. The aqueous catholyte comprises an evaporative-loss resistant and/or polyprotic active compound or active agent that partakes in the discharge reaction and effectuates cathode capacity for discharge in the acidic region. This leads to improved performance including one or more of increased specific energy, improved stability on open circuit, and prolonged cycle life, as well as various methods, including a method of operating an aqueous Li/Air cell to simultaneously achieve improved energy density and prolonged cycle life.