Water-in-water (W/W) emulsions show a characteristic decrease of the viscosity with increasing shear rate that is well described by equations proposed in the literature. Confocal laser scanning microscopy images showed that the decrease of the viscosity was caused by deformation and alignment of the dispersed droplets followed by string formation. W/W emulsions stabilized by the addition of polysaccharides or protein microgels still form strings when sheared with the particles remaining at the interface. After cessation of the flow, the strings break up into small droplets and the presence of stabilizing particles inhibits their coalescence. It is shown how the viscosity and the microstructure depend on the initial droplet size, the interfacial tension, the viscosity of the two phases, and the concentration of the stabilizing polymers.