Spatial Direct Numerical Simulations (DNS) were performed to investigate Laminar– turbulent transition for a flared cone at Mach 6. The flow parameters used in the simulations closely match the laboratory conditions of the hypersonic transition experiments conducted at Purdue University. The objective of the present research is to make a contribution towards understanding of the nonlinear stages of transition in hypersonic boundary layers on a flared cone. In particular, towards understanding the effect of the adverse pressure gradient on the nonlinear stages of transition. To this end, the role of second–mode fundamental (K-type) and oblique breakdown is investigated using controlled transition simulations. For fundamental resonance, the parameter space was first explored by performing several low-resolution simulations in order to identify the cases that result in the strongest nonlinear interactions. Subsequently, a set of highly resolved fundamental and oblique breakdown simulations have been performed and the results are presented in this paper. Both second–mode fundamental and oblique breakdown lead to strong nonlinear interactions and were thus found to be viable candidates of nonlinear mechanisms that can lead to a fully turbulent boundary layer. The nonlinear interactions observed during these breakdown processes are discussed in detail. A detailed description of the flow structures that arise due to these nonlinear interactions is provided and the development of the skin friction and heat transfer during the breakdown is presented.