Sustainability is a process that characterizes in a broad sense a nation’s ecological performance and may display a time-varying pattern. Such dynamic trajectories may vary among different countries and prompt not only intriguing questions on space–time convergence but also on the possibility of club convergence. The scope of this study is to investigate the long-run convergence pattern of 137 countries, as presented by their sustainable development index (SDI) over the period 1990–2019. The statistical–econometric analysis used to identify convergence across (groups of) countries is based on the advanced Phillips and Sul (JAE 24:1153–1185, 2009; ECTA 75:1771–1855, 2007) method. The empirical findings from our study allow us to identify two SDI convergence clubs of countries. The first and the biggest club includes mainly the developing African and Asian countries; whereas, the second club includes many OECD countries including inter alia the US, Canada, and Australia. Our analysis brings to light that the transition paths of these two clubs show a significant divergence pattern; this a-symmetry calls also into question the effectiveness of global green policies, such as the clean development mechanism as foreseen in the Kyoto protocol.