Direct numerical simulations are employed to investigate ‘natural’ laminar-turbulent transition in three-dimensional incompressible boundary layers with favorable-pressure gradients. Toward this end, the evolution of three-dimensional wave packets in swept laminar boundary layers is investigated, where the wave packets are generated by a localized short-duration pulse disturbance. First, the weakly nonlinear development of a wave packet in a two-dimensional zero-pressure gradient boundary-layer, guided by the wind-tunnel experiments of Gaster & Grant (1975), served as a validation for a Navier-Stokes solver based on a disturbance flow formulation that was developed in our laboratory. Next, the development of a wave packet in a three-dimensional boundary-layer initiated by a small amplitude pulse was examined. It was found that both stationary and traveling crossflow modes were generated with wide range of spanwise wavenumbers, with traveling modes reaching the largest maximum amplitude. By increasing the pulse forcing amplitude, the nonlinear evolution of the wave packet was investigated. Fourier decomposition clearly indicates a cascade of nonlinearly generated higher harmonics of the primary unsteady crossflow disturbances. Nonlinear mechanisms eventually trigger the transition process and the final breakdown to turbulence.