A new method to analyze materials exploring the quasilinear oscillatory regime has been described. One of its advantages is a significant reduction of the number of rheological tests needed, as compared to the originally proposed quasilinear large-amplitude oscillatory shear flow method. Furthermore, the authors improved the data analysis to a great extent, rendering it quite straightforward and physically sound. To validate the new method, we used two materials of qualitatively different rheological behavior, namely, a commercial hair gel and a solution of polyacrylamide in water/ glycerol. The data obtained are presented in two distinct forms. The first one uses either the traditional Kelvin-Voigt analysis-which yields as material functions the storage and loss moduli G' and G '', respectively-or the traditional Maxwell analysis, which yields as material functions the storage and loss compliances J' and J '', respectively. The second form originates from a Jeffreys analysis, which gives as output two material functions, namely, the relaxation time.1 and the retardation time.2. The results of the different analyses are compared and discussed. (c) 2019 The Society of Rheology.