New classes of compliant long dwell mechanism designs are introduced, formulated, and simulated. These classes of compliant dwell mechanisms incorporate the buckling motion of flexible members. Long dwell motion is obtained throughout the buckling motion of a flexible follower. Flexible buckling members are modeled using polynomial functions fitted to nonlinear inextensible exact elastica theory. The displacement analysis of the mechanisms is done quasi-statically using loop closure theory, static equilibrium of flexible parts represented by polynomial load deflections. One example of each new mechanism and its simulation results are presented.