Abstract: A characteristic feature of hyperbolic systems of balance laws is the existence of non-trivial equilibrium solutions, where the effects of convective fluxes and source terms cancel each other. Recently a number of so-called well-balanced schemes were developed which satisfy a discrete analogue of this balance and are therefore able to maintain an equilibrium state. In most cases, applications treated equilibria at rest, where the flow velocity vanishes. Here we present a new very high order accurate, exactly well-balanced finite volume scheme for moving flow equilibria. Numerical experiments show excellent resolution of unperturbed as well as slightly perturbed equilibria.