Upon approaching the liquid-vapor critical point, the spontaneous density fluctuations in a small-molecule fluid increase in both size and lifetime. Similar increases of the concentration fluctuations occur near the critical mixing point of a binary liquid mixture. The presence of these large fluctuations leads to an increase of the zero-shear viscosity, and their persistence in time leads to viscoelasticity and shear thinning. These theological phenomena, which are already supported by theory and experiment, are shown here to obey a generalized form of the Cox-Merz rule. This relation formally equates the shear viscosity eta(gamma) measured at shear rate gamma with the magnitude of the linear complex viscosity eta*(omega) measured at frequency omega. Comparisons of theoretical results and experimental data obtained elsewhere demonstrate that fluids near a critical point obey the somewhat generalized form eta(k(CMgamma) = omega) = \eta*(omega)\, with k(CM) = 0.4. The demonstration is simplified by showing that the Carreau-Yasuda model in the form (1 + bA (gamma)\gammatau\)(-P) represents the theories for eta(gamma) and \eta*(omega)\ near critical points. (The product bAgammatau is a time constant, and p = 0.022 is a universal critical exponent.). (C) 2004 The Society of Rheology.