The effects of interfacial viscosity on the droplet dynamics in simple shear flow and planar hyperbolic flow are investigated by numerical simulation with diffuse interface model. The change of interfacial viscosity results in an apparent slip of interfacial velocity. Interfacial viscosity has been found to have different influence on droplet deformation and coalescence. Smaller interfacial viscosity can stabilize droplet shape in flow field, while larger interfacial viscosity will increase droplet deformation, or even make droplet breakup faster. Different behavior is found in droplet coalescence, where smaller interfacial viscosity speeds up film drainage and droplet coalescence, but larger interfacial viscosity postpones the film drainage process. This is due to the change of film shape from flat-like for smaller interfacial viscosity to dimple-like for larger interfacial viscosity. The film drainage time still scales as Ca-0 at smaller capillary number (Ca), and Ca-1.5 at higher capillary number when the interfacial viscosity changes. The interfacial viscosity only affects the transition between these limiting scaling relationships. (C) 2008 Wiley Periodicals, Inc.