Droplets in microfluidic systems can contain microscale objects such as cells and microparticles. The control of the positions of microscale objects within a microchannel is crucial for practical applications in not only continuous-flow-based but also droplet-based systems. This paper proposes an active method for the separation of microparticles inside moving droplets which uses travelling surface acoustic waves (TSAWs). We demonstrate the preconcentration and separation of 5 and 10 mu m polystyrene microparticles in moving water-in-oil droplets through the application of TSAWs with two different frequencies. The microparticles inside the droplets are affected by the acoustic radiation force induced by the TSAWs to move laterally in the direction of the TSAW propagation and are thereby separated according to their size. In-droplet separation is then demonstrated through droplet splitting at a Y-junction. Compared to our previous studies, this acoustic approach offers the label-free and on-demand separation of different-sized micro-objects in moving droplets. The present method has potential uses such as in-droplet sample purification and enrichment. Published by AIP Publishing.