The paper presents some approaches for the design of a diagonal Proportional-Integral-Derivative (PID) controller for a two-input two-output TITO) system. First, a new autotuning procedure is given for a TITO system and from the results of this a design method is developed based on moving the critical point to a desired position on the compensated characteristic loci. Second, an optimisation method using integral performance criteria is presented. Examples are given to illustrate both design methods.