When a small drop or bubble approaches a fluid–fluid interface, a thin liquid film forms between them, drains, until an instability forms and coalescence occurs. A hydrodynamic theory is developed for the first portion of this coalescence process: the drainage of the thin liquid film while it is still sufficiently thick that the effects of London-van der Waals forces and electrostatic forces can be ignored. The time rate of change of the film profile is predicted, given only the drop radius and the required physical properties. Comparisons are offered with the limited experimental data available.