Joint value creation plays an important role in the transition to a more sustainable society. During such a process, conflicting interests, powers, speeds and priorities lead to tensions. Participants in the Circular Innovation Program, revolving around circularity focussed collaborative business modelling processes with 10 high-tech supply-chains, report such tensions. They are critical for the success, yet there is lack of recognition and support for the tensions they experience. Authors describe such tensions also in other domains. Tensions can follow from difficult choices or paradoxes. Paradoxes can be seen as "contradictory yet interrelated dualities that exist simultaneously and persist over time; such elements seem logical when considered in isolation, but irrational […] when juxtaposed.” (Smith & Lewis, 2011), and choosing is actually counterproductive. Beyond the classification of Smith & Lewis (2011) and the management strategies of Poole & Van de Ven (1989), focussed on single organisations, there is a scarcity of research specifically on how to categorize inter-organizational paradoxes, how they evolve and on which paradoxical tensions are experienced by participants. The objective of our overarching study is to assist participants in classifying and managing paradoxical tensions. In this paper, we present the exploratory stage for our design research, answering “What tensions do participants experience during Collaborative Sustainable Business Modeling and how do they deal with them?”. This study consists of consultation of 5 experts in the field, and semi-structured interviews with 20 boundary workers, representing 5 readily committed organizations and 3 supply-chain initiatives.