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In this paper, we develop an explanation for why events in one market may trigger similar events in other markets, even though at first sight the markets appear to be only weakly related. We allow for escape dynamics in each market, and show that an escape in one market is contagious because it more than doubles the probability of a similar escape in another market. We claim that contagion is strong since escapes become highly synchronised across markets. Spillovers are weak because the instantaneous spillover of events from one market to another is small. To illustrate our result, we demonstrate how a currency crisis may be contagious with only weak links between countries. Other examples where weak spillovers would create strong contagion are various models of monetary policy, imperfect competition and endogenous growth. (Copyright: Elsevier)