We explore exhumation in the coastal Kwanza Basin by combining analyses of Tertiary hiatuses and apatite fission tracks. Planktonic biozones show five major hiatuses in the Oligo-Miocene and Plio-Pleistocene. Between gaps, Oligo-Miocene strata accumulated under marine conditions. A marine setting refutes the idea of a massively raised coastal plateau in the mid-Tertiary. Marine conditions continued until ~5 Ma. Fission track data suggest three thermal events: ~150 Ma, during rifting and volcanism; ~100--70 Ma, during shortening and volcanism; and ~20--10 Ma, during exhumation. Tertiary uplift was spatially highly variable. For the Kwanza Basin, we infer that Tertiary uplift on the West African margin is indeed a fact but that estimates of uplift timing and size are unreliable when extrapolated to adjoining areas. Massive uplift (2000--4000 m) of the Precambrian craton had little structural effect in the outer basin. Instead, minor uplifts on the shelf drove late Tertiary deformation on the slope.