Spain is an ageing country, and the present demographic burden is not homogeneously distributed across space. Will the aged population be evenly distributed in the future, or will disparities broaden over time? Identifying the spatial patterns of the aged population concentration and the existence of a demographic burden convergence/divergence process is a pertinent question in Spain after the regional devolution the country has undergone in the last decades and the coexistence of different regimes. In this paper, we use a non‐parametric approach (geographically weighted regressions) to identify the determinants of the ageing dynamics, checking for the existence of a convergence/divergence ageing process after controlling for the socio‐economic characteristics of the Spanish municipalities. Although global estimations support the convergence hypotheses posed, GWR results show a significant variability of the effects depending on the area considered, which calls for a careful treatment of the results both for analysis and policy purposes.