In this article, we focus at a key concept of today's healthcare, namely responsibility. Personal responsibility is so important today because it is obvious that the way society is organized, many people are facing a lot of difficulties to live their lives in a responsible way. We explicitly obtain an analysis of responsibility from a view which avoids the binary thinking which is so remarkably present in today's health care discourse. The aim of this pilot study is therefore to open up the horizon of the use of responsibility in today's healthcare. We develop the notion of 'co-responsibility' to understand how individuals, despite the fact they are responsible for their own agency, are always also affected by an ought which contaminates their efforts to fulfill their duties and obligations. We discuss co-responsibility not as conclusion or a magic formula to all problems, but as a new starting point of which we have to explore the opportunities for current and future health care dilemmas.