The introduction of telehealth-care technologies profoundly changes existing practices of care. This paper aims to enhance our understanding of these changes by providing a comparative study of health-care services for heart-failure patients based on face-to-face contacts in a policlinic (department of a health care facility treating outpatients) and remote consultations at a telehealth-care centre. I will show how changes that take place when care moves from physical to virtual clinical encounters cannot be understood in terms of a replication of existing health-care services. Instead, it is more useful to conceptualise these health-care provisions as practices that create and value other kinds of care, incorporating different forms of proximity to patients. The physical proximity created at the policlinic facilitates contextualised, personalised care in which responsibilities for monitoring are delegated to nurses and patients and heart failure is constituted as an illness. The digital proximity that characterises the telehealth-care centre supports individualised, immediate care in which responsibilities are largely delegated to technological devices and heart failure is constituted as a disease. A major policy implication of these differences is that telehealth-care cannot simply replace physical consultations without changing the nature of health care.