The aging of family caregivers who provide care to adults and elderly people with intellectual disabilities brings a new reality that implies long-term care. Considering the issue of long-term care, family caregivers will probably at some point need support in providing care to their member with intellectual disabilities. Therefore, this research aimed to gain an insight into the perspective of family caregivers about the support they need, so that they can continue to provide adequate care to their members with intellectual disabilities due to aging. The aim of this study was to identify what types of support family caregivers need to provide adequate care. The research that was conducted was of a qualitative type. Five family caregivers participated in it. The semi-structured interview method was used for data collection, and the data processing method was thematic analysis. The thematic analysis resulted in three thematic areas corresponding to the research questions. The results of data processing indicate that with age, changes in health and behavior most often occur in people with intellectual disabilities. The aforementioned changes affect the increase in the scope of the necessary support provided by family caregivers. Furthermore, the extent of the demands of care, the loss of a close family member, old age and health changes with age, among family caregivers, can affect the reduction of their possibilities in providing adequate care to their members with intellectual disabilities. The good health of the family caregiver and informal support were seen as favorable factors in coping with caregiving demands. The majority of family caregivers expressed the need for formal support from a personal assistant. Also, the need for a center with day care services was expressed; for greater financial compensation for caregiver status; for the services of a professional service for the disabled, in the field of health care, for support in transportation and accompanying to therapies. All the mentioned formal supports would provide relief from the demands of care. The aforementioned findings suggest that the good health of family caregivers, formal and informal support, and the absence of challenging behaviors can be key in the ability to provide adequate care in young old age. Taking into account the above, formal support should supplement the existing gaps, but one should think longer term and find ways to preserve the health of caregivers and support the development of informal support networks.