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Compared to conventional viscometers, microacoustic viscosity sensors operate with small vibration amplitudes but at very high oscillation frequencies. Hence, the liquid under investigation is being probed in a fundamentally different manner: Whereas classical viscometers tend to uncover nonlinear behavior of the liquid, the microacoustic method primarily detects the onset of viscoelastic (frequency-dependent) behavior. Both effects, representing deviations from the idealized, linear, and instantaneous rheological behavior of liquids, are generally classified as "non-Newtonian." In this paper, we investigate the rheological behavior of different groups of oil-based liquids, which are important in a number of industrial applications, where we utilize both the conventional and the microacoustic method. It is shown that electrical insulation oils feature Newtonian behavior for both measurement approaches. On the contrary, engine, silicone, and vegetable oils, which are more complex in their chemical composition, all exhibit non-Newtonian behavior in terms of nonlinear as well as viscoelastic behavior.