During detachment folding, the relationship between differential uplift and shortening depends on the mechanism of fold growth, such as limb rotation or hinge migration, and may vary over the lifetime of a fold. Thus, neither long-term shortening rates nor the present fold geometry unambiguously constrain the kinematics of fold growth. Where rivers cut through growing anticlines, flights of abandoned fluvial terraces act as passive kinematic markers. As shortening progresses, the terraces become deformed and thereby preserve critical information about the kinematics and evolution of active fold growth. To constrain recent fold growth across three detachment folds in the Kashi-Atushi fold system in the SW Tian Shan, China, we surveyed flights of deformed terraces and compared them with geometric models of successively emplaced horizontal unconformities (terraces) across pregrowth strata deformed by hinge migration, limb rotation, and a combination of the two. Migration of angular hinges and curved hinge zones were also compared. Each kinematic model predicts both a distinct geometry for the deformed terraces and contrasting angular relationships between the terraces and the pregrowth strata. Notably, limb rotation and migration of curved hinge zones result in progressively rotated terraces that cut across pregrowth strata, whereas all limb-lengthening models result in parallelism between pregrowth strata and terrace straths across much of the fold. The Kashi-Atushi terraces show clear evidence of abandoned axial surfaces, concentrated deformation near the core of the folds, and progressive tilting with age. When compared to the model predictions, the folds are likely growing by a combination of limb rotation in the tight cores of the folds and hinge-zone migration of pregrowth strata across the flanks of the folds.