Helical geometries to induce swirling and spiral flow in prosthetic grafts have been hypothesized as a possible way to improve the clinical outcomes in patients undergoing coronary artery bypass grafting. In this paper, the transient flow behavior in helical bypass conduits with two different curved flow paths (planar and nonplanar) was investigated. Numerical methods were used to examine the flow physics downstream of four idealized bypass conduits attached to an aorta. The flow field in the bypass conduits was examined based on a non-Newtonian blood-analog fluid with relevant physiological waveforms characterized by a Womersley number α of 2.13 and a mean Reynolds number Remean of 107. The effects of nonplanar curvature and helicity were studied independently based on four idealized grafts. For all models, the axial flow downstream of the grafts resembles the oscillatory flow in straight tubes with a low α. The local secondary flow structures correspond closely to the strength of the swirling flow induced by the helical geometry. The helical conduit with a planar curved flow path in general consists of a pair of asymmetric vortices downstream. The introduction of a nonplanar curved flow path significantly increases the degree of asymmetry and leads to the transition from a double-vortex structure to a single swirling vortex flow. It is demonstrated that the swirling flow induced by the planar curvature promotes greater in-plane mixing downstream of the graft than the nonplanar curvature. However, the analysis of hemodynamic parameters reveals the effectiveness of a nonplanar curved flow path in the helical conduit in significantly elevating the overall mean wall shear stress. These findings demonstrate the possibility of using helical geometries and nonplanar curved flow paths in the design of external stents to independently control the mixing behavior and hemodynamic environment in coronary bypass conduits.