A full characterization of accessibility is provided for nonlinear time–delay systems. It generalizes the rank condition which is known for weak controllability of linear time-delay systems, as well as the celebrated geometric approach for delay free nonlinear systems and the characterization of their accessibility. Besides, fundamental results are derived on integrability and basis completion which are of major importance for a number of general control problems for nonlinear time–delay systems. They are shown to impact preconceived ideas about canonical forms for nonlinear time–delay systems.