Analysis of two examples of obliquely convergent external orogenic zones, the western part of the Western Carpathians and the northern Variscan margin in southwest Britain, indicates the operation of two dominant stress rotation mechanisms in the transpressionally deformed thrust wedge: (1) the rotation of an inferred stress field; (2) the rotation of a deforming body within a constant stress field. In the thinnest, external parts of the thrust wedge, σ1 stress trajectory rotations of up to 90° occur with deformation having a relatively small component of pure shear. Towards the hinterland, σ1 stress trajectories in thicker parts of the wedge are progressively less rotated but develop a larger component of pure shear. Resultant σ1 trajectories are curvilinear, lying parallel to the orogenic convergence vector in the hinterland but diverging progressively from this direction towards the foreland, where they lie at high angles to the external margin in frontal parts of the thrust wedge. It is argued that balanced cross-sections should be constructed parallel to the curved trace of the σ1 stress trajectories.