In this paper we investigate the return and volatility spillovers among equity and bond markets in the UK, USA, Germany and Japan, using continuous time models and discrete time multivariate GARCH modelling methods. Using weekly data over the period 2001 to 2011, empirical evidence of uni- and/or bi-directional return and volatility spillovers is provided. The continuous time analysis finds evidence of feedback effects in some cases. The discrete time results provide weak evidence of return spillovers, while volatility transmission among the majority of equity and fixed income markets is verified. Evidence shows that some of these relationships change in the post-crisis period.