The Smoluchowski approach for treatment of diffusion-controlled coagulation is modified to include the case of coalescing emulsion droplets which can deform before flocculation or coalescence. By using appropriate expressions for the droplet interaction and boundary conditions of Smoluchowski type, we calculate the distance at which the droplet deformation takes place, the nonequilibrium (but steady) radial distribution function, and the total force (including the ensemble averaged Brownian force) acting between the droplets. As a result the particle flux toward a given central'' droplet, i.e. the coalescence rate, is determined. The influence of different factors (Hamaker constant, surface potential, interfacial tension, drop size, and others) is investigated numerically.