Machine learning approaches are being developed to contribute to the treatment of patients and the organisation of care. These new approaches are created in complex environments that include data and computational models as well as new practices, roles and competencies. In such settings, individualised conceptions of agents bearing responsibility need rethinking. In response, we elaborate on the concept of epistemic responsibility based on De la Bellacasa’s work on care (Bellacasa, M.P. de la. (2017). Matters of care: Speculative ethics in more than human worlds. University of Minnesota Press). To better understand these complex environments and the dynamics of responsibility, we use an ethnographic approach and followed Dutch healthcare professionals who learned the basics of (supervised) machine learning, while they pursued a project in their organisations during a four-month-long course. The professionals struggled with different interdependencies and this brought responsibility-in-the-making into relief. Rather than seeing (growing) relations and impure entanglements as standing in the way of responsibility, we show how connections are worthy of inquiry. We argue that connections are essential to knowledge and that producing epistemic responsibility means considering these embedded relations. In contrast to calls for control and clarification of machine learning techniques, and warnings that they create irresponsible black boxes, our care approach shows how responsibility-in-the-making reveals opportunities for ethical reflection and action. Our approach attends to how humans and non-humans are engaged in caring, reveals patterns around kinds of responsibility, and points to opportunities for avoiding neglect and irresponsibility.