The Stokes boundary layer for a thixotropic or antithixotropic fluid

► We study mathematically the Stokes layer for a thixotropic or antithixotropic fluid. ► At low amplitudes of oscillation, distinct fast and slow responses are possible. ► Antithixotropic but not thixotropic fluids develop a boundary layer of finite width. ► Thixotropy affects the wall shear stress only weakly except near shear reversal. ► The behaviour depends subtly on how the structure kinetics are specified.