We first discuss wave propagation perpendicular to a magnetic field. Variables depend on x only. The medium is collision-free, described by the Vlasov theory. We can prove that there exist two, and only two, unique constants of the motion, that are independent of y, z and t, and that at least one of them depends on x. Thus a necessary condition for the existence of stationary shocks is fulfilled. Examples show that the existence proof also suggests a practical tool for solving problems. The oblique case which is also briefly discussed turns out to be qualitatively different in that, owing to the presence of reflected particles, a uniform upstream state cannot be prescribed a priori.