We report the dynamics of compound droplets with a denser liquid (water) droplet over a less dense sessile droplet (mineral oil) that satisfies the Neumann condition. For a fixed size of an oil droplet, depending on the size of the water droplet, either it attains the axisymmetric position or tends to migrate toward the edge of the oil droplet. For a water droplet-to-oil droplet at volume ratio V-w/V-o >= 0.05, stable axisymmetric configuration is achieved; for V-w/V-o < 0.05, migration of water droplet is observed. The stability and migration of water droplets of size above and below critical size, respectively, are explained using the force balance at the three-phase contact line and film tension. The larger and smaller droplets that initially attain the axisymmetric position or some radial position, respectively, evaporate continuously and thus migrate toward the edge of the oil droplet. The radial location and migration of the water droplets of different initial sizes with respect to time are studied. Experiments with water droplets on a flat oil-air interface did not show Migration, which signified the role of the curved oil-air interface for droplet migration. Finally, coalescence of water droplets of size above the critical size at the axisymmetric position is demonstrated. Our compound droplet studies could be beneficial for applications involving droplet transport where contamination due to direct contact and pinning of droplets on solid surfaces is of concern. Migration and coalescence of water droplets on curved oil air Interfaces, could open new frontiers in chemical and biological applications including multiphase processing and biological interaction of cells and atmospheric chemistry.