The influence of a hysteretic damper on the airfoil flutter instability is investigated. In particular, its effect on the post-critical limit cycle oscillations (LCOs) is emphasized. For that purpose, an aeroelastic model including large amplitude motions and dynamic stall phenomenon, is considered for a rigid flat plate having two degrees of freedom in pitch and plunge motions. The hysteretic behaviour is modeled thanks to a generalized Bouc-Wen formulation. A parametric study of aeroelastic as well as hysteresis model parameters, allows one to draw a complete picture of the bifurcation scenario, highlighting the capacity of the hysteretic damper in precluding the occurrence of stall. The special case of shape memory alloy (SMA) springs is then used numerically and experimentally for controlling the flutter oscillations of a flat plate. The study reveals the ability of the SMA springs to drastically reduce the amplitudes of the LCOs caused by the flutter instability.