A direct yaw moment control (DYC) for energy-efficiency and a DYC for stability of electric vehicles (EVs) are proposed. The DYC for energy-efficiency is active during non-safety-critical cornering manoeuvres to improve the energy-efficiency of EVs. The DYC for stability is active during safety-critical manoeuvres to keep the vehicle stable. A combination of the DYC for energy-efficiency and the DYC for stability is studied. A stability judgement based on the yaw rate and slip angle is designed for evaluating the criticality of the vehicle's working state. A switching principle for alternating between the DYC for energy-efficiency and the DYC for stability is designed. During non-safety-critical cornering manoeuvres, it is shown that the DYC for energy efficiency can save considerable percentage of energy compared to both equal torque driving and the DYC for stability. During cornering manoeuvres containing both non-safety-critical parts and safety-critical parts, the simulation results in this work show that the combination of the DYC for energy-efficiency and the DYC for stability can give 12% to 18% energy savings compared to the DYC for stability only for the vehicle and manoeuvres studied.