In this paper, we analyze the behavior of low-molecular-weight non-Newtonian fluids (liquid paraffin, silicone oil, and FC70 oil) in which the shear thinning phenomenon is observed at low shear rates. Over a wide range of a high shear rate, the behavior is described, which is similar to the Newtonian behavior in the case when the shear viscosity is practically constant. In terms of the structural rheological model, an explanation is proposed for this type of the Newtonian flow.