Let G be a Lie group with Lie algebra L(G) and let $Omega$ be a nonempty subset of L(G). If $Omega$ is interpreted as the set of controls, then the set of elements attainable from the identity for the system $Omega$ is a subsemigroup of G. A system $Omega$ is called a non-overlapping control system if any element attainable for $Omega$ is only attainable at one time.