In this work, the rectilinear How of a complex liquid under a pulsating, time-dependent pressure gradient is analyzed. The fluctuating component of the pressure gradient is assumed to be of small amplitude and can be adequately represented by a weakly stochastic process, for which a quasi-static perturbation solution scheme is suggested. The pulsating pressure-gradient flow is analyzed with the Bautista-Manero-Puig model (BMP) constitutive equation, consisting in the upper convected Maxwell equation coupled to a kinetic equation to account for the breakdown and reformation of the fluid structure. According to the BMP model, thixotropy was found to have a negative effect on the energy associated to the maximum flow enhancement and reflects the relationship among the kinetic, viscous and structural mechanisms in the system. The flow enhancement is a function of the square of the amplitude of the Reynolds and Weissenberg numbers, and it is also dependent on the dimensionless the oscillations, numbers representing the viscoelastic, kinetic and structural mechanisms. Finally, flow enhancement is predicted in an aqueous worm-like micellar solution of cetyltrimethyl ammonium tosilate (CTAT) for various concentrations. (C) 2009 Elsevier B.V. All rights reserved.