The breakup process of primary drops during transition through slots or small openings has been examined frequently in the past. Recent experiments show strong influence of the dispersed-phase viscosity on the deformation of drops at the inlet of orifices that cannot be explained by the equilibrium approach based on capillary numbers or viscosity ratios only. It is necessary to account for the strongly transient character of the process. A quantitative treatment of this behavior based on relationships from the literature and executed with feasible numerical effort is presented. It is shown that the course of the extension rate of the flow and all properties of the system have a major influence on the drop deformation in front of the orifice. The threadlike deformed drops are precursors for the subsequent breakup process downstream.