The laminar breakdown of a three-dimensional flat-plate boundary-layer flow with favourable and ensuing adverse pressure gradient (APG), generic for an infinite swept wing, is investigated in detail by means of spatial direct numerical simulations. Emphasis is on transition mechanisms in the region of adverse pressure gradient where the undistorted laminar base flow also becomes unstable with respect to Tollmien–Schlichting (TS) waves that are most amplified if two-dimensional with respect to the local streamwise direction. The influence of finite-amplitude crossflow vortices, coming from the region of favourable pressure gradient, on the TS instability properties is investigated. It turns out that crossflow-vortex-induced secondary instabilities are the most amplified disturbances even for low-amplitude vortex modes. The TS waves act as generators of fundamental low-frequency secondary modes, but are neither important for their growth nor for breakdown. As for active disturbance control, any method aiming at attenuating two-dimensional TS waves must fail. On the other hand, the passive upstream-flow-deformation technique also delays transition in the APG region.