Abstract. A non-parametric rank-based test of exchangeability for bivariate extreme-value copulas is first proposed. The two key ingredients of the suggested approach are the non-parametric rank-based estimators of the Pickands dependence function recently studied by Genest and Segers, and a multiplier technique for obtaining approximate p-values for the derived statistics. The proposed approach is then extended to left-tail decreasing dependence structures that are not necessarily extreme-value copulas. Large-scale Monte Carlo experiments are used to investigate the level and power of the various versions of the test and show that the proposed procedure can be substantially more powerful than tests of exchangeability derived directly from the empirical copula. The approach is illustrated on well-known financial data.