“Wave” fields have long been recognized in marine sediments on the flanks of basins and oceans in both tectonically active and inactive environments. The origin of “waves” (hereafter called undulations) is controversial; competing models ascribe them to depositional processes, gravity-driven downslope creep or collapse, and/or tectonic shortening. Here we analyze pervasive undulation fields identified in swath bathymetry and new high-resolution multichannel seismic (MCS) reflection data from the Sea of Marmara, Turkey. Although they exhibit some of the classical features of sediment waves, the following distinctive characteristics exclude a purely depositional origin: (1) parallelism between the crests of the undulations and bathymetric contours over a wide range of orientations, (2) steep flanks of the undulations (up to ∼40°), and (3) increases in undulations amplitude with depth. We argue that the undulations are folds formed by gravity-driven downslope creep that have been augmented by depositional processes. These creep folds develop over long time periods (≥0.5 m.y.) and stand in contrast to geologically instantaneous collapse. Stratigraphic growth on the upslope limbs indicates that deposition contributes to the formation and upslope migration of the folds. The temporal and spatial evolution of the creep folds is clearly related to rapid tilting in this tectonically active transform basin.