Building on Giraud & Tsomocos (2009), we develop a model of non equilibrium international trades with incomplete markets. Trades occur in continuous time, both on international and domestic markets. Traders are assumed to exhibit locally rational expectations on future prices, interest rates and exchange rates. Although currencies turn out to be non-neutral, if their stock grows sufficiently rapidly and if agents can trade assets during a sufficiently long period, the world economy converges in probability towards some interim constrained efficient state. Moreover, a random localized version of the Quantity Theory of Money holds provided the economy is not trapped in a liquidity hole. The traditional theory of comparative advantages, however, turns out to be challenged by international capital mobility.Currency, cash, liquidity, monetary policy, money, international trade, quantity theory of money, transition to equilibrium.