New equations for the viscosity of concentrated double emulsions of core-shell droplets are developed using a differential scheme. The equations developed in the paper predict the relative viscosity (eta(r)) of double emulsions to be a function of five variables: a/b (ratio of core drop radius to shell outer radius), lambda(21) (ratio of shell liquid viscosity to external continuous phase viscosity), lambda(32) (ratio of core liquid viscosity to shell liquid viscosity), phi(DE) (volume fraction of core-shell droplets in double emulsion), and phi(m)(DE) (the maximum packing volume fraction of un-deformed core-shell droplets in double emulsion). Two sets of experimental data are obtained on the rheology of O/W/O (oil-in-water-in-oil) double emulsions. The data are compared with the predictions of the proposed equations. The proposed equations describe the experimental viscosity data of double emulsions reasonably well.