Internally oscillating cycles of cutting and filling occur naturally in many coupled geomorphic systems. As a demonstration, we have modeled stream entrenchment and backfilling where alluvial systems couple to uplifting mountain blocks. This simple model tracks bedrock stream erosion and transport of alluvium to base level. Internal oscillations arise from coupling of a kinematic wave model for mountain erosion to a diffusion model for the alluvial basin. Decaying periodic cutting and filling occur on time scales of 105 yr; the largest magnitudes are found at the coupling point. Model results suggest that cyclic sedimentation may result from the tintinnabulation of single perturbations applied to natural systems and need not record cyclic changes in climate, tectonics, or base level.