The antifoaming of aqueous surfactant solutions by mixtures of nonpolar oils and hydrophobic solid particles was investigated and a new mechanism was suggested. According to this mechanism, the antifoam drops containing the particles flow from the lamellae of a static foam into its plateau borders and get trapped there. The trapped oil drops enter the bubble surfaces and form lenses because the pseudoemulsion films, i.e., the aqueous films between the antifoam drops and the gas phase, are destabilized by the solid particles. On further foam drainage these lenses get trapped in the thinning plateau borders and form a bridge whereby the hydrophobic particles destabilize the film between the lens and the opposite surface of the plateau border. The driving force of the antifoaming action is the capillary pressure in the plateau borders of foam. Antifoaming by oil alone is much less effective because the process is controlled by the instability of the pseudoemulsion film and, without hydrophobic particles, this film is stable. The hydrophobic particles alone are less effective than the mixture because the particles alone penetrate less into the aqueous phase than the oil + solid lenses. For high efficiency, the antifoam drops must be large enough because smaller drops are less likely to get trapped in the plateau borders. The effect of oil viscosity, the presence of solid particles in the oil, and the antifoam deactivation process on the antifoam drop size and activity are discussed.