The majority of non-Newtonian materials exhibit an out-of-phase stress-strain relationship (i.e., evidenced by the fundamental and associated harmonics) over a wide range of frequencies. This nonlinear response of the material when subjected to a periodic disturbance of amplitude γ, say, may be due in part to viscoelasticity, thixotropy, or a combination of the two. Other factors such as particle size and concentration can also contribute to this effect. Apparatus has been developed which enables harmonic analysis to be carried out with comparative ease in the low to mid-frequency range; the nonlinear response of a material offers no experimental problems. The experimental work reported here on a soap and synthetic base grease confirms the views that: Greases are nonlinear viscoelastic in response over the whole range of strain amplitude, frequencies, and temperatures investigated. Particle size and concentration are observed to influence the flow stability of each grease. At small strain amplitudes the synthetic base grease is mainly elastic in response, but the stress moves out-of-phase with strain as the strain amplitude is increased. The behavior of the stress fundamental component suggests yielding of the structure. The harmonic content appears to be more sensitive to changes in strain amplitude and temperature than the fundamentals. The method of reduced variable has been applied to the fundamental and associated harmonics with reasonable success, supporting the implications of this method that increasing the temperature is equivalent to decreasing the frequency. An approximate method of correlating dynamic and steady shearing motion results in terms of the function α (phase shift in dynamic response) is outlined, the resulting correlation being difficult to apply mainly because of the mathematical shortcomings.