The nonlinear stability analysis of a liquid film composed of two superposed thin layers of immiscible liquids resting on a solid substrate is performed. It is shown that the coupling of van der Waals interactions in the two layers can lead to an autophobic behavior in the form of spinodal decomposition of two planar liquid layers into a system of localized drops divided by almost planar wetting layers. The results of the weakly nonlinear analysis near the instability threshold are confirmed by the numerical solution of a system of two strongly nonlinear evolution equations for the liquid-liquid and liquid-gas interfaces. The kinetics of the drop coarsening at late stages is studied and is found to be close to that reported for a one-layer film. It is also shown that gravity effects can become significant even for very thin two-layer films. (c) 2005 Published by Elsevier Inc.