This chapter tries to highlight how the three core process of innovation should be organized and managed when the open innovation process concerns direct rivals. We will try to show how OI between competitors impacts each of the three OI process and leads to new potentially fruitful research areas. We will also try to define a research program for OI involving full collaboration with competitors, in the outside-in from a competitor, the inside-out to a competitor and the coupled-innovation process between competitors. We name this strategy Open Coopetition and use OI and coopetition literatures to highlight the main promising research avenues leaded by this new concept