This paper studies a New Keynesian model of a two-country world with a zero lower bound (ZLB) constraint for nominal interest rates. A floating exchange rate regime is assumed. The presence of the ZLB generates multiple equilibria. The two countries can experience recurrent liquidity traps induced by the self-fulfilling expectation that future inflation will be low. These "expectations-driven" liquidity traps can be synchronized or unsynchronized across countries. In an expectations-driven liquidity trap, the domestic and international transmission of persistent shocks to productivity and government purchases differs markedly from shock transmission in a "fundamentals-driven" liquidity trap.JEL codes: E3, E4, F2, F3, F4 Keywords: Zero lower bound, expectations-driven and fundamentals-driven liquidity traps, domestic and international shock transmission, terms of trade, exchange rate, net exports.(*) I thank Chris Erceg (discussant), Tom Holden and Werner Roeger for advice. Helpful comments were also received from Tobias Broer, Raf Wouters and participants at the Belgian Macro Workshop and at the European Commission-CEPR-JEDC conference on "Secular Stagnation and Low Interest Rates".