Abstract In this paper, the damping properties of presliding hysteresis are explored for the LuGre and Maxwell-slip friction models. Taking out of consideration the classical linear viscous damping and Stribeck effect, the nonlinear damping of force–displacement hysteresis is analyzed, in Lyapunov sense, for the motion dynamics. Based thereupon the simple but straightforward criteria of model’s parametrization are derived for kinetic friction to be dissipative. Further we show a related experimental example of presliding hysteresis friction response in vicinity to zero velocity.