In this paper, we consider a class of optimal control problem with discrete-time delayed arguments and bounded control regions. A conditional gradient algorithm has been obtained by Wong and Teo for solving this class of optimal control problem. It is also shown that any Lx accumulation points of the control sequences generated by the algorithm satisfy a necessary condition for optimality. Since such accumulation points need not exist, it is shown that control sequences generated by the algorithm always have accumulation points in the sense of a control measure, and that these accumulation points satisfy a necessary condition for optimality for the corresponding relaxed problem.