The theory of non-commutative rings is introduced to provide a basis for the study of nonlinear control systems with time delays. The left Ore ring of non-commutative polynomials defined over the field of meromorphic function is suggested as the framework for such a study. This approach is then generalized to a broader class of nonlinear systems with delays that are called generalized Roesser Systems. Finally, the theory is applied to analyze nonlinear time-delay systems. A weak observability is defined and characterized, generalizing the well-known linear result. Properties of closed submodules are then developed to obtain a result on the accessibility of such systems.