What are the relevant management challenges for open innovation, and how do companies tackle these challenges? This study adds to the research of open innovation management by investigating different management dimensions and their inherent dilemmas. By applying the concept of organizational ambidexterity as an approach to pursue apparently conflicting objectives, we extend previous research in two key aspects: First, in contrast to most studies we do not focus on a single management dimension but consider a wider set of dimensions which we found evidence to be relevant for open innovation. Second, unlike previous studies which consider ambidexterity for managing open innovation, we do not limit our discussion to ambidexterity as a whole but consider different modes of ambidexterity. Our findings support this approach: We find structural ambidexterity for the degree of innovation, organizational configuration, intellectual property management and motivation. We also find temporal and contextual ambidexterity in two additional dimensions.