The aim of this paper is to generalize some ideas related to the concept of causality in General Relativity and to carry them over to the theory of control systems. Suppose that M is a smooth manifold, and let (Sigma) (q) over dot = f(u)(q), u is an element of U, be a control system on M satisfying certain natural conditions. It is proved that if F : M -> M is a bijection such that F and F-1 map the trajectories of (Sigma) onto trajectories of (Sigma) then F is a homeomorphism.