Using a quasi-steady, blade-element analysis, we investigated the role of asymmetrical flapping mechanisms in hovering flight, for insect inspired micro air vehicles. The current analysis was applied to a 30 cm half-span wing, beating not more than 6 Hz. An implementation of asymmetrical flapping exhibited significantly greater lift generation, which can be attributed to the increase in angular velocity squared form for lift that occurs with increasing asymmetry. Significant improvements in the lift-to-power ratio were observed, for a house-fly-like mode of flapping, when the wing-beat frequency was below the natural frequency. At a frequency ratio of 0.3, a 75% increase in performance was observed with the use of asymmetrical flapping. At flapping frequencies above the natural frequency, however, asymmetry was found to be detrimental to performance, due to an increase in inertial forces. In a low inertia, an inclined stroke plane system, characteristic of dragonflies, we see that, in its most efficient flapping condition, asymmetrical flapping is detrimental to performance. However, in compliant systems in which elastic forces are significant, we see that asymmetry can improve the aerodynamic efficiency of the wing-actuation system.