The spatial evolution of the disturbances that lead to boundary-layer transition on a swept wedge is computed by large-eddy simulations (LES). Stationary and travelling crossflow-vortex disturbances are generated using steady and random-amplitude suction and blowing on the wedge. For a fixed initial amplitude of the stationary vortex and low-amplitude unsteady disturbances, the LES show the evolution of stationary-dominated crossflow disturbances similar to previous simulations and experiments: linear amplification is followed by vortex roll-over and doubly inflectional velocity profiles just prior to transition. A high-frequency secondary instability is associated with the double inflection points in the velocity profiles. The harmonic modes of the primary disturbance were found to be amplified, while no energy was found in any subharmonic mode. The physical phenomena were significantly different when the stationary and travelling vortices have comparable initial amplitudes: in this case, the vortex roll-over does not occur and transition is dominated by the travelling-wave component.