Analytic and numerical modeling indicates that melting of xenoliths in magmas may be controlled by viscous flow. The xenolith melt will be removed immediately by the host magma if flow is present and new xenolith melt can be produced. This melting mechanism is referred to as ablation. Ablation dominates the melting process in earlier experiments in the system diopside. We propose that complex phases (solid solutions) undergo ablation when the heat flow into a xenolith is high. Ablation is found to be controlled by a nearly linear rate law after a short heating up period. The average computed ablation rates coincide with earlier experiments of diopside. We predict steady state ablation rates at 20 K superheating for β-cristobalite (3.8¿10-4 m/s), high-sandine (1.6¿10-4 m/s), calcite (4.9¿10-5 m/s), clineonstatite (4.0¿10-5 m/s), and forsterite (3.2¿10-5 m/s). A cold xenolith might cool down the host liquid next to it below the glass transition temperature and to accrete a glassy crust. Such chilled selvage accretion will modify the total assimilation rates of granulites by less than 10% for xenolith radii <20 cm. Ablation appears to be more effective as compared to diffusion controlled assimilation. This could explain the worldwide predominance of mafic and ultramafic (mantle and lower crust) compared to felsic lower crustal xenoliths. ¿ American Geophysical Union 1993