Snap‐off is an important dynamic multiphase flow phenomenon which occurs in porous media. It plays a dominant role in the residual trapping and mobilization/immobilization of nonwetting fluids such as hydrocarbons or CO2. Current studies, applications, and threshold criteria of snap‐off are mostly based on static or equilibrium conditions. Thus, the dynamics of snap‐off which is relevant for many real world applications has rarely been systematically studied. While a static criterion indicates the snap‐off potential for nonwetting fluids, the competition between the time required for snap‐off and the local pore throat capillary number determines whether snap‐off actually occurs. Using a theoretical model to couple the wetting film thickness to the local capillary number at the pore throat, we analyzed the dynamics of the wetting/nonwetting interface instability in sinusoidally constricted capillary tubes. The influence of dynamic factors as encapsulated by the effect of local capillary number on nonwetting fluid snap‐off time were investigated for varying pore throat to pore body aspect ratio and pore body distances. The analysis showed that snap‐off can be inhibited by a sufficiently large local capillary number even in cases where the static snap‐off criterion has been met. Key Points: Large local capillary number can inhibit snap‐off occurrence Snap‐off time is calculated against controlling parameters Snap‐off process is coupled with film thickness