We use a fully coupled asymmetric dynamic finite element model to study interactions between thermomechanical behavior and surface processes during continental rift evolution. The model accounts for (1) nonlinear brittle-elastic-ductile rheology, layered lithological structure, and faulting; (2) heat transport and thermal buoyancy forces; and (3) true erosion and sedimentation (grid elements are eliminated and recreated). Faults are not predefined but are self-localized; their distributions and geometry are model outputs, which provides new geologically sensible constraints on its validity. We test previous ideas on rift evolution based on numerical and analytical component theories (or individual parts) of our model. After demonstrating that our coupled model reproduces classic rift features, we then demonstrate that synrift surface processes result in enhanced lithospheric thinning and widening of the basin, so that the apparent stretching factors increase by a factor of 1.5--2. Sedimentation results not only in thermal but also in localized flexural weakening of the lithosphere, which locally compensates strengthening due to cooling. Erosion on the uplifted flanks produces local strengthening and rebound. Surface processes produce pressure gradients, which drive a ductile crustal flow that (1) provides a fast feedback with tectonic processes and controls subsidence rates and flank stability and (2) drives a secondary extension or compression and uplift on the late synrift/early postrift phase. Our results indicate that kinematic and dynamic rift models that ignore erosion may produce misleading results in many rifts. We reproduced and explained a number of enigmatic synrift phenomena, such as (1) polyphase subsidence provoked by switching of the level of necking between different competent lithological layers and (2) synrift and postrift stagnation and vertical accelerations unassociated with tectonic stress inversion or phase changes. ¿ 2001 American Geophysical Union