We study the dynamics of a compound liquid drop which is comprised of an outer membrane surface, a shell layer, and a core. The deformation due to an imposed extensional flow and the subsequent recovery are investigated computationally employing a combined Eulerian–Lagrangian technique. The numerical method allows for large viscosity and capillarity differences between layers. The present study reports several findings which provide direct insight into developing a dynamic model for leukocytes. A compound drop behaves like a homogeneous, simple liquid drop if the core is sufficiently deformed and the time scale of the core, related to the combination of its viscosity and capillarity, is comparable to that of the shell layer. Disparate time scales between the core and shell layer result in a rapid initial recoil of the drop during which the shell fluid is the primary participant in the hydrodynamics, followed by a slower relaxation period during which the core and shell layer interact with each other. Consequently, the apparent viscosity of the drop depends not only on the rheological properties of the drop, but also on the flow dynamics surrounding it. The findings obtained with the three-layer compound drop model can explain several main characteristics of leukocytes reported in the literature. Furthermore, our study suggests that unless the presence and possible deformation of the nucleus are explicitly accounted for, neither Newtonian nor non-Newtonian models for leukocytes can adequately predict the hydrodynamics of leukocytes. ©1998 American Institute of Physics.