Let Ф : f0; 1gn ! f0; 1gn be a function whose coordinates Фi; i 2 f1; :::; ng are iterated independently on each other, in discrete time or real time. The resulted flows, called asynchronous, model the asynchronous circuits from the digital electrical circuits. The concept of double eventual periodicity refers to two eventually periodic simultaneous phenomena, one of the function (so called computation function) indicating when and how Ф is iterated and the other one of the flow itself. The paper introduces the double eventual periodicity of the asynchronous flows and gives two important results on them.