Abstract: The major-to-minor axis ratio is a key geometric parameter affecting boundary-layer transition on conical high-speed vehicles, with a particularly pronounced influence on three-dimensional boundary-layer structures such as streamwise vortices. To explore the underlying mechanisms, this study obtains the base-flow by directly solving the Navier–Stokes equations, and employs two-dimensional global stability analysis (Bi-Global) to systematically investigate the instability characteristics of streamwise vortices over an elliptic cone at various major-to-minor axis ratios. The freestream Mach number is 6, the static temperature is T_\mathrme = 52 K, the unit Reynolds number is Re_\rmunit=1.02\times10^7/m, and the wall temperature is T_\mathrmw = 300 K. The model has a nose radius of 1 mm, a semi-cone angle of 7^\circ along the minor axis, and major-to-minor axis ratios e of 1.25, 1.5, 2.0, and 4.0. The base-flow results show that at e=1.25, a low-speed streak forms along the centerline of the elliptic cone. When the major-to-minor axis ratio increases to 1.5, the low-speed streak rolls up on both sides, giving lift-up to mushroom-shaped streamwise vortices. As the ratio increases further, the spanwise rolling-up of the streamwise vortices becomes more intense, their formation shifts upstream, and their streamwise development and evolution accelerate. Stability analysis reveals that at e=1.25, the dominant mode along the centerline is the symmetric Mack mode. When the ratio increases to 1.5, the Mack mode dominates upstream, with a maximum N factor reaching 8. Further downstream, as the streamwise vortices roll up into mushroom shapes, unstable outer modes emerge in the boundary layer. Among these, the symmetric Y mode, dominated by wall-normal shear, exhibits the highest growth rate and is most likely to trigger transition of the streamwise vortices, with a dominant frequency of 179 kHz. When the major-to-minor axis ratio increases to 4.0, the Z mode, dominated by spanwise shear, becomes the fastest-growing mode, and the mode most likely to induce transition shifts from the Y mode to the Z mode. Transition prediction based on the \rme^N method shows that a larger major-to-minor axis ratio yields a higher integrated N factor within the computational domain. This indicates that the larger the major-to-minor axis ratio, the farther upstream the streamwise vortex transition occurs, which is consistent with the formation characteristics of the streamwise vortices.