An aging population, a lack of qualified medical staff, and rising costs in the healthcare sector pose major challenges to many societies. Implementing digital solutions in hospitals is a promising response to these challenges without compromising the quality of patient care. Nevertheless, the adoption of digital solutions in the healthcare environment is progressing more slowly than might be desirable. Adopting a paradox perspective, we study tensions in the relationship between the providers of digital solutions and hospitals (their customers) that can explain the slow uptake. Drawing on 39 interviews, our findings reveal nine tensions related to the three dimensions of a business model (value proposition; value creation and delivery; value capture). We also identify four coping strategies that allow solution providers to deal with these tensions, especially when building digital solutions in new ecosystems. The strategies to cope with paradoxical tensions in interorganizational relationships include accommodation, avoidance, concession, and confrontation.