Reducing the detector thickness to mono-and bilayers of WSe2 only weakly decreases the response speed, rendering WSe2 advantageous over MoS2 for fast optical communication. Further miniaturizations of the device geometry have the potential for Gigahertz photodetection with such easily fabricated WSe2 photodetectors which exhibit long-term stability under ambient conditions. In addition to the non-ohmic behaviour, the flake shows a slight asymmetry which can be caused by different heights. 1