We study international risk sharing and international transmission in a model with within and between countries incomplete markets (uninsurable risk and borrowing constraints), with one or two assets. We show that incomplete markets induce a wedge in the aggregate risk-sharing condition. When income risk is countercyclical the wealth effects and the precautionary motives induce a time-varying disconnect that can reconcile statistics related to international risk-sharing: high consumption growth leads to expected appreciations, the correlation between the marginal utilities (or consumption) across countries and the real exchange rate is negative and in the same magnitude as in the data, cross-country consumption correlation is lower than that of output, the exchange rate is highly persistent.