For two main reasons optimal tuning the (PID mu)-D-lambda controllers is a challenging task: First, the search space is very large in dealing with such controllers, and second, there is not any generally applicable method for stability testing of the linear feedback systems containing both time delay and fractional-order controllers. Hence, easy-to-use and effective rules for optimal tuning such controllers are highly demanded. In this paper, explicit formulas for optimal tuning the parameters of the (PID mu)-D-lambda controller, when it is applied in series with a first-order plus time-delay process in a standard output-feedback system, are proposed. (c) 2012 Canadian Society for Chemical Engineering