I develop a two-country New Keynesian model with capital accumulation and incomplete international asset markets that provides novel insights on the effect that imperfect international risk-sharing has on international business cycles and RER dynamics. I find that business cycles appear similar whether international asset markets are complete or not when driven by a combination of non-persistent monetary shocks and persistent productivity (TFP) shocks. In turn, international asset market incompleteness has sizeable effects if (persistent) investment-specific technology (IST) shocks are a main driver of business cycles. I also show that the model with incomplete international asset markets can approximate the RER volatility and persistence observed in the data, for instance, if IST shocks are near-unit-root. Hence, I conclude that the nature of shocks, the extent of financial integration across countries and the existing limitations on asset trading are central to understand the dynamics of the real exchange rate and the endogenous international transmission over the business cycles.