A two-dimensional kinematic model, which incorporates lateral accommodation of extension and differential stretching, is used to investigate the geodynamic evolution of the Valencia trough. This Neogene basin, located between the Iberian Peninsula and the Balearic Promontory, underwent two rifting episodes, the first one being coeval with compression. Model predictions are compared with observations of tectonic subsidence, Bouguer gravity anomaly, surface heat flow, and the present-day crustal structure. The best fitting model assumes three stages in the evolution of the basin. During the first stage (late Oligocene-early Miocene), extension is mainly restricted to the central and northwestern parts of the basin, whereas its southeastern margin is locked by the Alpine deformation front. The material expelled from the axial area is partly accommodated under the Balearic Promontory, producing compression and crustal thickening. During the second rifting stage (middle Miocene), extension affects a much broader area, including the Balearic Promontory and the Algero-Proven¿al basin. The third stage (late Miocene to Recent) corresponds to a postrift thermal relaxation phase. Our results put further constraints on the geodynamic evolution of the area. ¿ 1999 American Geophysical Union