In all societies, the human life cycle is characterized by stages of dependency and periods of net production that lead to inter-generational transfers of resources. We present the first global estimates of ‘sandwichness’, the situation of simultaneously having frail older parents and dependent young children or grandchildren, for the 1970-2040 cohorts using demographic methods and microsimulations calibrated with data from the 2019 United Nations World Population Prospects. We find that sandwichness is more prevalent in the Global South - people born in 1970 Sub-Saharan Africa are twice as likely to be `sandwiched' than Europeans - but it is expected to decline globally by one third between 1970 and 2040. The Global North might have reached a peak in the simultaneous demands on care-time from multiple generations. Nevertheless, grandparents in the Global South will increasingly spend more time sandwiched between parents and grandchildren, potentially increasing their involvement in care responsibilities.