Abstract: The complex viscosity of a material is a two-component quantity, comprising real and imaginary parts. The real part of the complex viscosity is often very useful because in many materials it approaches the ordinary steady-flow viscosity at low frequencies. Because many materials with high viscosities are very slow in reaching a steady-flow condition, the determination of the steady-flow viscosity may be very difficult; however, an approximation can often be obtained from low-frequency values of the real part of the complex viscosity. In this study, the complex viscosity of a Georgia kaolin has been determined by measurements made on specimens subjected to oscillatory simple shear, over three decades of frequency. Other independent variables in the study are the water content of the clay and the shear strain amplitude. Data were obtained from experimental measurements in the form of values of the magnitude, or absolute value, of the complex viscosity, and the phase angle between the imposed oscillatory strain and the stress response. Empirical functional relationships are developed to relate these quantities to the independent variables, and these are in turn used to obtain the real and imaginary parts of the complex viscosity as functions of the independent variables. The results of this study indicate that the complex viscosity is not linear, but decreases approximately as a power function of the strain amplitude; the relation between the complex viscosity and the water content is approximately an inverse logarithmic one, and changes very rapidly at water contents near the liquid limit; and the phase angle increases with increasing strain amplitude approximately as a power function.