Structural investigations in post-obductional Paleocene to Eocene limestones of the Tertiary Ridge reveal a ~1 km long WNW-ESE striking strike-slip fault system within the ridge, consisting of two main sub-parallel, strike-slip faults. Considering the geometry of the Harding Strain Ellipse, the orientation of structures between the two strike-slip faults (e.g., Riedel shears, folds, reverse faults) point to left-lateral motion. The abundance of large-scale folds (up to 100 m in wave length and amplitude) between the two strike-slip faults led us to the interpretation of transpressive conditions in a first approximation. Moreover, the Tertiary Ridge of the study area consists of three distinct structural domains. The faults of Domain A and C are oriented WNW-ESE, but the trend of the faults in the central Domain B differs by ~10°. The left-lateral strike-slip fault system exists only in Domain B. We propose that the direction of greatest stress during Miocene plate convergence (sigma 1) was oriented 032°/212°. Considering the trend of the strike-slip zone and the orientation of sigma 1, the left-lateral motion must have been transpressive. Sigma 1 is perpendicularly oriented to the domains A and C. Prior to the Miocene D2 compressional event the study area was affected by a D1 extensional event, related to the opening of the Red Sea and the Gulf of Aden or to gravity-driven normal faulting. The D2 compressional/transpressional structures of the Miocene are reactivating the D1 structures of the Oligocene.