Many metastable complex fluids, when subjected to oscillatory shear flow of increasing strain amplitude at constant frequency, are known to show a characteristic nonlinear rheological response which consists of a monotonic decrease in the elastic modulus and a nonmonotonic change in the loss modulus. In particular, the loss modulus increases from its low strain value, crosses the elastic modulus, and then decreases with further increase in the strain amplitude. Miyazaki et al. (Europhys Lett 75:915-921, 2006) proposed a qualitative argument to explain the origin of the nonmonotonic nature of the loss modulus and suggested that in fact this response could be universal to all complex fluids if they are probed in a certain frequency window in which the fluid is dominantly elastic in the small strain limit. In this letter, we confirm their hypothesis by showing that a wide variety of complex fluids, irrespective of their thermodynamic state under quiescent conditions, indeed show the aforementioned characteristic nonlinear response. We also show that the maximum relative dissipation during yielding occurs when the imposed frequency resonates with the characteristic beta relaxation frequency of the fluid. © 2013 Springer-Verlag Berlin Heidelberg.