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This work addresses the robust control of processes of the form G (s) = K · e − τ · s / (1 + T · s λ) with 1 < λ ≤ 2 . A new method for tuning fractional-order P I and P D controllers is developed. The stability is assessed based on the frequency domain tuning of the regulators to control such delayed fractional-order underdamped processes. In order to analyze the closed-loop stability and robustness, the new concept of Robust High-Frequency Condition is introduced. The analysis based on that demonstrates that each controller has a different region of feasible frequency specifications, and, in all cases, they depend on their fractional integral or derivative actions. Finally, an application example, the position control of a teleoperated manipulator with a flexible link, is presented. Simulations and experiments illustrate that the region of feasible frequency specifications defined at low and high frequencies allows us to obtain robust controllers that fulfill frequency requirements. [ABSTRACT FROM AUTHOR]