Résumé : We employ a two-stage general dynamic factor model method to analyse the co-movements between returns and between volatilities of stocks belonging to the US, European, and Japanese financial markets. We find evidence of two common shocks driving the dynamics of volatilities - one global (worldwide) shock and one US-European shock and four "national" shocks in the panel of returns, but no global one. Co-movements in the returns and volatilities panels increased considerably in the period 2007-2012 associated with the Great Financial Crisis and the European Sovereign Debt Crisis. We interpret this finding as the sign of a surge, during crises, of interdependencies across markets, as opposed to contagion. Finally, we show that the global volatility shock, identified via natural timing assumptions, has homogeneous dynamic effects within each individual market but more heterogeneous effects across them, and also has good predictive power on aggregate realised volatilities.