In this paper, using an orthogonal curvilinear coordinate system and solving the complete N-S equations, we analyzed the flow in a helical elliptical duct by the perturbation method. The first-order solutions of the stream function Ψ, axial velocity w and the velocity of secondary flow (u, v) were obtained. The effects of torsion, curvature and the axial pressure gradient on the secondary flow were discussed in detail. The study indicates that the torsion has first-order effect on the secondary flow in a helical elliptical pipe, the secondary flow is dominated by torsion when the axial pressure gradient is small and for increasing gradient the secondary flow is eventually dominated by the effect due to curvature. The fact that the torsion has no effect on fluid flow in a helical pipe with a circular cross section was also confirmed. The most important conclusion is that the flow in a helical elliptical pipe to the first-order can be obtained as a combination of the flow in a toroidal pipe and the flow in a twisted pipe.