In this paper are reported the effects of prolonged soaking on a model system: nonpolar oil drops on fibrous polymer substrates immersed in aqueous solutions of various surfactants. In certain of these systems a layer of aqueous microdroplets grew on the surface of the fiber, beneath the oil drops. Addition of sodium chloride to the bulk aqueous phase reversed this growth. The rate of growth increased with increasing solubility of water in the oil. It also increased when an oil-soluble surfactant was added to the system. Addition of a surfactant that was not oil-soluble (SDS) produced no such effect. An explanation of these phenomena is advanced in terms of the Kelvin equation. Secondary oil droplets, surrounding the main oil drop, appeared in some systems. These can be attributed to an effect of capillarity, oil spreading out from the central oil drop in microgrooves on the fiber surface. Naturally occurring oils and fibers and certain osmotic effects which may operate in such systems are also discussed.