Research on autocracies has gained new momentum in the last decade. One element of this research is the observation that some autocracies are characterised by structural conditions that are normally conducive for democracy. These ‘anomalous autocracies’ have high levels of socioeconomic development and democratic neighbour countries. The study of these cases might expose factors that are decisive for autocratic stability and studying them might give us a better understanding of barriers towards democratisation. This paper contributes to the growing literature on autocracies by mapping anomalous autocracies during the third wave of democratisation, thereby paving the way for systematic case selection in future studies. A large-N analysis of 159 cases (1975–2008) identifies Belarus, Chile, China, Cuba, Morocco, North Korea, Peru, Singapore, Swaziland, Togo and Zimbabwe. In a second step, the paper lays out a theoretical framework that centres on actors and institutions. Rulers must establish elite–elite and elite–mass interaction, and this papers argues that they can do so through quasi-compliance of elites and the masses based on traditional institutions woven into a dominant party. The paper uses the framework to tentatively examine the resilience of authoritarian rule in Swaziland and Morocco, two most-different anomalous cases. In both cases, an elaborate traditional institution has co-opted government, business and rural elites and coordinated interaction within elite circles and with the masses, in turn enabling the remarkable regime resilience.