The international literature shows that primary care is well placed to address mental health problems in young people, but that primary care professionals experience a range of challenges in this regard. In Denmark, young adults who have complex psychosocial problems, and who are not in education or work, cause political and academic concern. They are also in regular contact with their general practitioners, the Danish municipalities and psychiatric services. However, little is known about general practitioners' perspectives on caring for this vulnerable group of patients. In this article, we investigate how general practitioners' care work is shaped by the bureaucratic management of care in a complex infrastructure network comprising the general practitioners, psychiatry, the municipalities and the young adults. The analysis is based on interviews and focus groups with general practitioners, psychiatric nurses and social workers. We employ Tronto's concept of care and the concept of boundary work as a theoretical framework. We argue that general practitioners strive to provide care, but they are challenged by the following: contested diagnostic interpretations and the bureaucratic significance of diagnoses for the provision of care from psychiatry and the municipalities, systemic issues with handling intertwined social and mental health problems, and the young adults' difficulties with accessing and receiving available care.