Abstract - When a water drop falls onto an oil-water interface, the drop usually rests for some time before merging with the water underneath the interface. We report experiments on this process using water- and oil-based Newtonian liquids and polymer solutions, with an emphasis on the non-Newtonian effects. We find that the drop surface is immobilized, and for Newtonian fluids, the rest time scales with the matrix viscosity. The results are compared with lubrication models for film drainage. If the surrounding matrix is a dilute polymer solution, the rest time is identical to that for a matrix of the solvent alone. Further investigation indicates that the polymer molecules have been cleared from the film by surface adsorption. Depending on the fluid properties and drop size, the drop-interface merging may be completed in one shot or through a cascade of partial coalescence. Partial coalescence occurs for an intermediate range of drop sizes; it is arrested by viscosity for smaller drops and by gravity for larger ones. When either the drop or the matrix phase is a polymer solution, viscoelasticity is shown to suppress partial coalescence for smaller drops. This is apparently due to the inhibition of capillary pinch-off which would otherwise produce a secondary drop before the merging is complete.