This paper evaluates the international macroeconomic spillovers from the Eurosystem’s expanded Asset Purchase Programme (APP) under alternative assumptions as regards (i) the unwinding of the asset positions accumulated under the APP and (ii) the normalization of the US monetary policy stance. We simulate a dynamic general equilibrium model of the world economy, calibrated to the Euro area (EA), the US, China, Japan, and the ‘rest of the world’ (RW). Our results are as follows. First, APP expansionary spillovers are dampened if the Eurosystem brings forward the unwinding of its bond holdings because of the lower increase in EA aggregate demand and, therefore, EA imports. The RW is the region most affected because it has the greatest trade integration with the EA. Second, if the US monetary authority announces that it will hold the policy rate constant for a shorter period of time – which dampens the increase in US aggregate demand and, therefore, US imports from the EA – then US spillovers to the EA, while still expansionary, as in the case of a slower normalization of the monetary policy stance, are more modest.