A pair of oblique waves at low amplitudes is introduced in a supersonic at-plate boundary layer. Its downstream development and the concomitant process of laminar to turbulent transition is then investigated numerically using Direct Numerical Simulations (DNS). In the present paper, first the linear regime is studied in great detail. Comparisons to linear stability theory clearly determine that the so-called "oblique breakdown" mechanism is initiated. The focus of the second part is the nonlinear regime. It is shown how the spectrum is filled up by nonlinear interactions, what flow structures arise and how these structures locally break down to small scales. Finally, a logarithmic region of the mean streamwise velocity profile is formed indicating the beginning of a fully turbulent flow region. The simulations demonstrate that oblique breakdown is a viable path to turbulence.