The deformation, drainage and rupture of the film of a Newtonian fluid between colliding drops of a power-law liquid is studied numerically for gentle constant-force collisions at small Reynolds numbers. The wholeshear-thinning range of the power-law parameter, n, is investigated, together with a range of transformed dispersed to continuous-phase viscosity ratios, *, covering the transition from partially mobile to immobileinterfaces. The problem is solved numerically by means of a finite-difference method for the equations in the continuous phase and a finite-element method for the non-Newtonian flow in the drops.The final stage of drainage is well described by a power-law empirical dependence of the minimum film thickness on time for the whole range of (*; n) values investigated. The boundaries! of the partially mobile,transitional and immobile drainage region in (*; n) plane as well as the coefficients of the empirical dependence are obtained. The application of the results for power-law drops to practically more relevant generalviscous dispersed phases is discussed.The rupture of the film due to van der Waals forces is studied for a wide range of the transformed Hamaker constant, A*, including both `rim' and `nose' rupture modes. The results indicate that the transformed criticalrupture thickness, hc*, is only weakly dependent on the non-Newtonian flow in the drops, being primarily determined by A*, as predicted by the approximate relation given in [A.K. Chesters, Trans. Inst. Chem. Engrs.Part A 69 (1991) 259¯270].