Using data for over four decades, we examine the ageing of Swedish municipalities and if there has been convergence or divergence across time and space, where we differentiate across the urban–rural hierarchy. As migration is claimed to be a moderating factor in the ageing of places, we assess how the share of immigrants relates to ageing patterns. Our findings show that the share of older individuals increases in more peripheral localities and that there has been convergence across municipalities. However, the share of foreign population is negatively related to the ageing profile of a place. © 2023 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.