Iterative learning control (ILC) is one of the recent topics in control theories and it is a powerful control concept that iteratively improves the behavior of processes repetitive in their nature. ILC is suitable for controlling a wider class of mechatronic systems - it is especially suitable for the motion control of robotic systems that attract and hold an important position in technical systems involving control applications, military industry, etc. This paper addresses the problem of iterative learning control (ILC) for fractional nonlinear time delay systems. Particularly, we study fractional order time delay systems in the state space form with unknown bounded constant time delay as well as time-varying delay. Sufficient conditions for the convergence of a proposed  type of a learning control algorithm for a class of fractional state space time delay systems are presented in the time domain. Also, a feedback-feedforward  type robust iterative learning control (ILC) of the given fractional order uncertain time delay system is considered. We consider fractional order time delay systems in the state space form with uncertain bounded constant time delay in particular. Sufficient conditions for the convergence in the time domain of the proposed ILC are given by the corresponding theorem together with its proof.Finally, a simulation example shows the feasibility and effectiveness of the proposed approach

Key words: theory of control, iterative control, learning control, fractional order, nonlinear system, time delay, robotic system.