Optimal control functions in the sense of minimum settling time and minimum fuel or energy consumption are derived for several different single-axis attitude control systems. The systems treated differ only in the mechanism used to produce control torque. The torque producing elements considered include, (i) reaction gas jets, with either one or two discrete levels of thrust, (ii) an armature controlled d-c motor, (iii) a two-phase a-c motor. Optimal switching curves for these systems are illustrated in the phase plane, and the optimal choice of system parameter values is discussed.