Dynamics of compound droplets consisting of more than two liquids is of engineering importance, in particular to bio-medical applications. This work reports a numerical study on the deformation and breakup of such compound droplets. An OpenFOAM based Coupled Level VOF finite volume solver was used in this study. A 2D axisymmetric isolated droplet consisting of two fluids was taken. Two set of simulations were performed. In the first case, the inner fluid was assumed to be Newtonian and the outer fluid was non-Newtonian. In the second set, the arrangement was reversed where the inner fluid was non-Newtonian and the outer fluid was Newtonian. In both cases, the non-Newtonian fluid was assumed to be a power-law fluid with a rheology of the form τ = Kýⁿ. The density ratio between the liquids is unity and the liquid to gas density ratio is 10³. The compound droplet was subjected to an ambient air flow stream. Effect of outer fluid film thickness and interfacial shear rate on droplet deformation and breakup for different Reynolds number is studied. Both shear thinning and shear thickening fluids were considered where the Power fluid index, n is varied in the range of 0.5 to 1.5. Detailed analysis of the flow field inside the droplet was also analyzed.