In this paper it is shown, for the first time, that a nonspreading oil can form films over water films present in the edges of pores in a water-wet porous medium. Both the water and the oil wet the solid surface preferentially to air, but water wets the solid preferentially to oil. The mechanism of the film formation is capillary imbibition, i.e., spontaneous displacement of air by the oil, and it is similar to the formation of water films in the edges of a clean glass capillary of angular cross section filled with air. The principal difference is that, whereas the water imbibes over a solid surface, the oil imbibes over a surface consisting partly of water and partly of a solid wetted by oil. It is shown, by a combination of applications of Laplace’s equation of capillarity with the condition of minimum surface free energy, that if a "critical" oil film thickness is exceeded by the addition of excess oil, then this excess oil will imbibe over the water film in the edge until the equilibrium critical oil film thickness is established. The equations have been solved by iteration for the critical oil film thickness, using representative values of the parameters involved. Further, it is shown that an oil blob placed in a capillary of polygonal (e.g., square or equilateral triangle) cross section, containing water films in the edges of the capillary, will imbibe in the form of films over the water present in the edges, subject to certain limitations, specified in the paper. The theoretical predictions are supported by photomicrographs showing imbibition of benzene equilibrated with water and a paraffin oil over water present in the edges of a 2D glass micromodel. The spreading coefficient is negative for both systems.