This thesis addresses dementia care in Sweden and the function family caregivers are given. The aim of the thesis is to analyse critically the system of municipal eldercare and the function of family caregivers in this system, and in various types of organisations. In the thesis, both organisational perspectives and the experiences of family caregivers are in focus. Eldercare has been a focus of the welfare state from its early days. Throughout the years both the organisation of care and the understanding of responsibility between family and state has changed several times. Today, family caregivers in Sweden have no formal responsibility for people with dementia, but many family caregivers still take on a caregiver responsibility. This raises questions about the function family caregivers play in dementia care and the reasons behind the choice of caregiving. The thesis consists of four papers on which a cumulative analysis was made. The empirical material is based on interviews with 146 family caregivers, of which 55 answered additional questions. Furthermore, a mapping study of activities and professional specialisation was used to study variations between municipalities. Text material was also utilised, both in the form of policies and formal documentation on a municipal level, and on research on family caregiving in dementia care on a national level. The cumulative analysis was made from the perspective of critical systems theory and resulted in three paradoxes: The welfare paradox, the value paradox and the responsibility paradox. The paradoxes are closely connected, and limit agency among family caregivers. Opposition in processes of familisation (the welfare paradox), individual values rather than family values (the value paradox), and the limitations in factual choice in taking on a caregiver responsibility (the responsibility paradox) cooperate in shaping the function of family caregiving and simultaneously limiting family caregiver agency. Since it is in the interest of dementia care to involve family caregivers the paradoxes also contribute to a solution to challenges in dementia care.