In this paper we study one specific type of non-technological innovation: strategic innovation. Strategic innovation follows a Schumpeterian perspective entailing a deviation from the traditional competitive rules of the game with the aim of offering a new and superior value proposition. As companies creating strategic innovations show high revenue and profit growth a deeper understanding of the underlying organizational capabilities would be highly relevant to both researchers and managers. Therefore, and in contrast to prevailing research on strategic innovation, we do not study the phenomenon on an industry level but study the capabilities that a business unit needs for the systematic creation of strategic innovations. More specifically, we study structural design capabilities and focus on the concept of 'ambidexterity'. The central theme in this nascent research stream is which (if any) organizational design allows firms to be efficient and adaptive/innovative at the same time. We use a two-phase qualitative design to study business units' systematic creation processes of strategic innovations in five Dutch industrial sectors. Our findings add to the emerging academic discussion on ambidexterity by showing that the appropriate ambidexterity approach may not only differ by innovation type but also by the specific phase of the innovation project. Our data show that companies have to cope with different ambidexterity frictions in the initiation and commercialization phases of strategic innovation projects. More specifically, the initiation phase rests on 'contextual ambidexterity': the initiation of strategic innovation initiatives is interwoven with the normal core business operations. To this end, companies establish mechanisms that stimulate the recognition and assimilation of customer/market knowledge. In contrast, 'structural ambidexterity' is applied during the commercialization phase, meaning that strategic innovations are gradually separated from the core business. These findings are relevant to managerial practice as they suggest a limited value of isolated business development units for strategic innovation initiation.