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Abstract. We introduce an Anosov action on the bundle of Weyl chambers of a riemannian symmetric space of non-compact type, which for rank one spaces coincides with the geodesic flow. IntroductionThe geodesic flow of a riemmanian symmetric space of non-compact type is an Anosov flow if and only if the rank of the space is one. In this note we shall introduce an action, which for spaces of rank one coincides with the geodesic flow, but which is Anosov for all riemannian symmetric spaces of non-compact type. The basic idea in defining this action is to view geodesies not as particular curves of the space, but as totally geodesic flat subspaces. So we are led to consider flats, i.e. maximal totally geodesic flat subspaces, and Weyl chambers as particular subsets of flats. The bundle of all Weyl chambers will be the phase space of the action. The geodesic flow is given by moving geodesic rays along their supporting geodesies. Similarly, the action to be denned here consists of parallel translating Weyl chambers within their supporting flats. If the rank of the space is one, then flats are geodesies, Weyl chambers are geodesic rays, and our action coincides with the geodesic flow. For spaces of rank higher than one, i.e. spaces with higher-dimensional flats, this action is no longer a flow, but an action of a higher-dimensional abelian Lie group.Let us recall the definition of an Anosov action (cf. [5]; for the ergodicity of Anosov actions, see [8]). An action