We propose a Bayesian time-varying model that learns about the dynamics governing joint extreme values over time. Our model relies on dual measures of time-varying extremal dependence, that are modelled via a suitable class of generalized linear models conditional on a large threshold. The simulation study indicates that the proposed methods perform well in a variety of scenarios. The application of the proposed methods to some of the world's most important stock markets reveals complex patterns of extremal dependence over the last 30 years, including passages from asymptotic dependence to asymptotic independence.