Vine copulae provide a graphical framework in which multiple bivariate copulae may be combined in a consistent fashion to yield a more complex multivariate copula. In this article, we discuss the use of vine copulae to build flexible semiparametric models for stationary multivariate higher‐order Markov chains. We propose a new vine structure, the M‐vine, that is particularly well suited to this purpose. Stationarity may be imposed by requiring the equality of certain copulae in the M‐vine, while the Markov property may be imposed by requiring certain copulae to be independence copulae.