The efficient interconversion of chemicals and electricity through electrocatalytic processes is central to many renewable-energy initiatives. The sluggish kinetics of the oxygen reduction reaction (ORR) and the oxygen evolution reaction (OER)(1-4) has long posed one of the biggest challenges in this field, and electrocatalysts based on expensive platinum-group metals are often required to improve the activity and durability of these reactions. The use of alloying(5-7), surface strain(8-11) and optimized coordination environments(12) has resulted in platinum-based nanocrystals that enable very high ORR activities in acidic media; however, improving the activity of this reaction in alkaline environments remains challenging because of the difficulty in achieving optimized oxygen binding strength on platinum-group metals in the presence of hydroxide. Here we show that PdMo bimetallene-a palladium-molybdenum alloy in the form of a highly curved and sub-nanometre-thick metal nanosheet-is an efficient and stable electrocatalyst for the ORR and the OER in alkaline electrolytes, and shows promising performance as a cathode in Zn-air and Li-air batteries. The thin-sheet structure of PdMo bimetallene enables a large electrochemically active surface area (138.7 square metres per gram of palladium) as well as high atomic utilization, resulting in a mass activity towards the ORR of 16.37 amperes per milligram of palladium at 0.9 volts versus the reversible hydrogen electrode in alkaline electrolytes. This mass activity is 78 times and 327 times higher than those of commercial Pt/C and Pd/C catalysts, respectively, and shows little decay after 30,000 potential cycles. Density functional theory calculations reveal that the alloying effect, the strain effect due to the curved geometry, and the quantum size effect due to the thinness of the sheets tune the electronic structure of the system for optimized oxygen binding. Given the properties and the structure-activity relationships of PdMo metallene, we suggest that other metallene materials could show great promise in energy electrocatalysis.