Abstract We establish several new characterizations of amenable $W^*$ - and $C^*$ -dynamical systems over arbitrary locally compact groups. In the -setting we show that amenability is equivalent to (1) a Reiter property (2) existence certain net completely positive Herz–Schur multipliers $(M,G,\alpha )$ converging point weak* identity $G\bar {\ltimes }M$ . -setting, prove $(A,G,\alpha an analog...