This paper presents a non-linear framework to evaluate spillovers across domestic and international yield curves when policy rates are constrained by the zero lower bound. Based on the sample of US and UK data, we estimate a joint shadow rate model of international yield curves, accounting for the zero lower bound, no-arbitrage conditions within and between government bond markets, and the global nature of some of the bond risk factors. Results indicate that the post-2009 US monetary policy transmission mechanism and its spillover effects on the UK yield curve are non-linear and asymmetric.