If two control systems on manifolds of the same dimension are dynamic equivalent, we prove that either they are static equivalent, i.e., equivalent via a classical diffeomorphism, or they are both ruled; for systems of different dimensions, the one of higher dimension must be ruled. A ruled system is one whose equations de. ne at each point in the state manifold a ruled submanifold of the tangent space. Dynamic equivalence is also known as equivalence by endogenous dynamic feedback or by a Lie-Backlund transformation when control systems are viewed as underdetermined systems of ordinary differential equations; it is very close to absolute equivalence for Pfaffian systems. It was already known that a differentially. at system must be ruled; this was a particular case of the present result, in which one of the systems was assumed to be "trivial" (or linear controllable).