Flies display a sophisticated suite of aerial behaviours that require rapid sensory-motor processing. Like all insects, flight control in flies is mediated in part by motion-sensitive visual interneurons that project to steering motor circuitry within the thorax. Flies, however, possess a unique flight control equilibrium sense that is encoded by mechanoreceptors at the base of the halteres, small dumb-bell-shaped organs derived through evolutionary transformation of the hind wings. To study the input of the haltere system onto the flight control system, I constructed a mechanically oscillating flight arena consisting of a cylindrical array of light-emitting diodes that generated the moving image of a 30 degrees vertical stripe. The arena provided closed-loop visual feedback to elicit fixation behaviour, an orientation response in which flies maintain the position of the stripe in the front portion of their visual field by actively adjusting their wing kinematics. While flies orientate towards the stripe, the entire arena was swung back and forth while an optoelectronic device recorded the compensatory changes in wing stroke amplitude and frequency. In order to reduce the background changes in stroke kinematics resulting from the animal's closed-loop visual fixation behaviour, the responses to eight identical mechanical rotations were averaged in each trial. The results indicate that flies possess a robust equilibrium reflex in which angular rotations of the body elicit compensatory changes in both the amplitude and stroke frequency of the wings. The results of uni- and bilateral ablation experiments demonstrate that the halteres are required for these stability reflexes. The results also confirm that halteres encode angular velocity of the body by detecting the Coriolis forces that result from the linear motion of the haltere within the rotating frame of reference of the fly's thorax. By rotating the flight arena at different orientations, it was possible to construct a complete directional tuning map of the haltere-mediated reflexes. The directional tuning of the reflex is quite linear such that the kinematic responses vary as simple trigonometric functions of stimulus orientation. The reflexes function primarily to stabilize pitch and yaw within the horizontal plane.