An alternative to the film-thinning model for coalescence of drops at the horizontal liquid-liquid interface has been proposed and elucidated through analysis of drop rest time distribution, both in the presence and absence of added surfactants. The model is based on the assumption that the drop rests at the interface as a result of the repulsive force generated by a high concentration of adsorbate molecules on the opposite faces of the barrier ring. The repulsive force could be DLVO type (double layer force) or non-DLVO type (hydration/steric). High concentration of the adsorbate builds up at the barrier ring during the approach of the drop at the interface, when the resulting shear displaces the adsorbate on the faces of the entrapped film towards the barrier ring. The repulsive force at the barrier ring decays with time, due to back-diffusion of the adsorbate towards the centre of the film. Coalescence occurs when the repulsive force at the barrier ring is too weak to support the weight of the drop. The major cause of the distribution of drop rest time during the experiment involving sequential addition of drops is the drop-to-drop fluctuation in the surface excess of the adsorbate. This fluctuation is caused by the interfacial disturbance resulting from coalescence of the previously added drops and also by non-uniform distribution of the adsorbate at the barrier ring. Based on these ideas, a mathematical model for the rest time distribution has been developed. The model fits well to our own experimental data and those reported in the literature. Validity of the model is established through comparison of the predicted trends of the rest time distribution, with those observed under a variety of experimental conditions. The evidence, which reveals the shortcomings of the currently accepted film-thinning model, has also been presented.