By analytically continuing the stress tensor evolution equation used in our previous studies of static phenomena in fluids and solving the equation, we have derived some analytic formulas for dynamic viscosities as functions of the amplitude and frequency of oscillating shear rate. They show markedly nonlinear rate dependencies different from those predicted by the linear theory. A set of approximate dynamic viscosity formulas (the first approximation) is used to derive a rule similar to the Cox–Merz rule, which is seen to be valid in the low frequency regime in the present approach. It is shown that the real and imaginary parts of the dynamic complex viscosity can be put into forms which depend on a reduced shear rate and a reduced frequency only, and therefore there exist corresponding states for the material functions. The formulas predict power laws in the high shear rate and frequency regimes which are quite reminiscent of those holding for some polymer solutions.