This paper investigates the mechanism for secondary recirculations in non-Newtonian flows in a noncircular pipe, and develops a general criterion on the direction of the secondary flow based on the fluid rheology and the cross-sectional geometry of the pipe. Although the secondary flow is usually attributed to the second normal stress difference N-2, the relationship between the two turns out to be more involved than previously assumed. By theoretical analysis and numerical computations using the Giesekus model, we show that N-2 produces an effective body force that, if nonconservative, gives rise to secondary flows in the transverse direction. From this understanding, we propose a criterion for the direction of the secondary flow based on the second normal stress coefficient Psi(2) and the shear viscosity eta(s): if Psi(2)((gamma)over dot)/ eta(s)((gamma)over dot) is an increasing function of the strain rate gamma, the fluid flows from high shear regions to low shear regions along the walls and vice versa. This criterion accounts for all the prior computational work and resolves some inconsistencies in the literature. It is also consistent with all experimental observations to date. (C) 2008 The Society of Rheology.