This paper explores the ability of common risk factors to predict the dynamics of US and UK interest rate swap spreads within a linear and a non-linear framework. We reject linearity for the US and UK swap spreads in favour of a regime-switching smooth transition vector autoregressive (STVAR) model, where the switching between regimes is controlled by the slope of the US term structure of interest rates. The first regime is characterised by a "flat" term structure of US interest rates, while the alternative is characterised by an "upward" sloping US term structure. We compare the ability of the STVAR model to predict swap spreads with that of a non-linear nearest-neighbours model as well as that of linear AR and VAR models. We find some evidence that the nearest-neighbours and STVAR models predict better than the linear AR and VAR models. However, the evidence is not overwhelming as it is sensitive to swap spread maturity. We also find that within the non-linear class of models, the nearest-neighbours model predicts better than the STVAR model US swap spreads in periods of increasing risk conditions and UK swap spreads in periods of decreasing risk conditions.