The effect of an adverse pressure gradient (without separation) on the downstream development of a wave packet in a flat plate boundary layer is investigated using threedimensional Direct Numerical Simulations (DNS) based on the incompressible Navier-Stokes equations. The wave packet was generated by a short duration pulse at the surface of the flat plate. Both the linear and nonlinear stages of the evolution of the wave packet were considered. For investigating the linear stages, the initial disturbance amplitudes were kept very small, whereas for investigating the nonlinear stages, larger amplitudes were used. The DNS results for the linear case are in very good agreement with Linear Stability Theory (LST) calculations. The pressure gradient was found to significantly increase the growth of instability waves compared to the case without pressure gradient. For the high-amplitude case, the strong disturbance growth and the ensuing nonlinear interactions quickly lead to the formation of a turbulent spot.