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A ``critical'' tracking task is developed in which a human operator is required to stabilize an increasingly unstable first-order controlled element up to the critical point of loss of control. Servo theory and operator describing function measurements are used to validate the basic assumptions, and an automatically paced critical task mechanization is described. The results show that the task does constrain the operator's behavior as intended, and that the critical instability depends primarily on the operator's effective time delay while tracking. A number of applications for the critical task are reviewed, including secondary workload research, control and measurement of operator and controlled element gain, and display research.