Here a conceptual framework is provided for analysing the role of the flight muscles in stability and control. Stability usually refers to the tendency of a system to return to a characteristic reference state, whether static, as in gliding, or oscillatory, as in flapping. Asymptotic Lyapunov stability and asymptotic orbital stability as formal definitions of gliding and flapping flight stability, respectively, are discussed and a limit cycle control analogy for flapping flight control proposed. Stability can arise inherently or through correctional control. Conceptually, inherent stability is that which would arise if all body parts were rigid and all articulation angles were constants (gliding) or periodic functions (flapping), both of which require muscular effort. Pose can be maintained during disturbances by neural feedback or isometric contraction of tonic muscles: cyclic pose changes can be buffered by neural feedback or viscous damping by phasic muscles. Correctional control serves to drive the system towards its reference state, which will usually involve a phasic response, if only because of the tendency of flying bodies to oscillate during disturbances. Muscles involved in correctional control must therefore be tuned to the characteristic frequencies of the system. Furthermore, in manoeuvre control, these frequencies set an upper limit on the timescales on which control inputs can be effective. Flight muscle physiology should therefore be evolutionarily co-tuned with the morphological parameters of the system that determine its frequency response. Understanding this fully will require us to integrate internal models of physiology with external models of flight dynamics.