Highly resolved Direct Numerical Simulations (DNS) are employed to investigate the hydrodynamic instability mechanisms and transition to turbulence in swept laminar separation bubbles that are generated on a flat plate by a displacement body in the free stream. A set of numerical simulations has been carried out to investigate the transition process, and in particular to shed light on the development of the large coherent structures, which arise during transition in three-dimensional and separated boundary layers. Four different sweep angles were considered: 0,15,30 and 45-degrees. The preliminary results show that the extent of laminar separation bubble in both streamwise and wall-normal directions was reduced as the sweep angle was increased to 30-degrees. When the sweep angle was increased even further the downstream length of the bubble remained unchanged. However height of bubble continued to decrease. For unswept separation bubble, transition involves a Kelvin-Helmholtz instability and a growth of three-dimensional low frequency perturbations in the shear layer. Boundary layers on swept flat plate are fundamentally different from their two-dimensional counterparts. They exhibit a crossflow velocity component, which can give rise to a crossflow instability due to the inflectional velocity profile that is generated by the crossflow. Our simulation results indicate that cross-flow instability mechanisms have a strong impact on the transition process for 30 and 45-degrees sweep such that transition was accelerated compared to the unswept case. In all of the present simulations no external disturbances w ere introduced into the boundary-layer to trigger the laminar-turbulent transition. Rather, transition to turbulence was self-sustained. In addition to DNS we employed a linearized Navier-Stokes solver to investigate the linear instability development, in particular with respect to the dominant steady crossflow modes.