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High-performance airfoils for transonic flows of Bethe-Zel'dovich-Thompson fluids are constructed using a robust and efficient Euler flow solver coupled with a multi-objective genetic algorithm. Bethe-Zel'dovich-Thompson fluids are characterized by negative values of the fundamental derivative of gasdynamics for a range of temperatures and pressures in the vapor phase, which leads to nonclassical gasdynamic behaviors such as the disintegration of compression shocks. Using Bethe-Zel'dovich-Thompson gases as working fluids may result in low drag exerted on airfoils operating at high transonic speeds, due to a substantial increase in the airfoil critical Mach number. This advantage can be further improved by a proper design of the airfoil shape, also leading to the enlargement of the airfoil operation range within which Bethe-Zel'dovich-Thompson effects are significant. Such a result is of particular interest in view of the exploitation of Bethe-Zel'dovich-Thompson fluids for the development of high-efficiency turbomachinery. [ABSTRACT FROM AUTHOR]