Abstract: The existence problem of optimal control systems described by x=f(t,x,u) is discussed in this paper, where f(t.x,u) is a more general function and the class of admissible control functions are general enough to contain those control functions which are frequently used in engineering. The problem for an optimal control approximated by a sequence of control functions being part of certain function classes is considered here, an example in contradiction with the conclusion of ref. [1] about this problem is given, and a correct conclusion is presented.