Through a lately developed boundary element method, this paper investigates the rheology of the multiple-emulsion globule with various internal structures in a contraction tube. As fine templates to prepare microcapsules for targeted drug delivery, multiple emulsions (ME) with complex structures have been generated through microfluidics. The deformation and breakup of multiple emulsions in a microchannel are critical to the transport and release of their inclusion. However, the numerical investigation of the rheology of multiple emulsions in a contraction tube is only limited to a simple case, i.e., core-shell double emulsions (CSDE), currently. In this paper, the boundary element method is employed to investigate the deformation and displacement of 2-dimensional globules of three types of multiple emulsions, i.e., concentric ME with multiple layers, double emulsions containing multiple inner droplets and ME with asymmetric internal structures, in a contraction tube. Comparing to those of CSDE, the complication of internal structures and the collision among inner droplets will subject the globule to flows with higher pressure drops when the volume flow rates are fixed. (C) 2013 Elsevier Ltd. All rights reserved.