We propose two related equilibrium refinements for voting and agenda-setting games. Sequentially Weakly Undominated Equilibrium (SWUE) and Markov Trembling Hand Perfect Equilibrium (MTHPE), and show how these equilibrium concepts eliminate non-intuitive equilibria that arise naturally in dynamic voting games and games in which random or deterministic sequences of agenda-setters make offers to several players. We establish existence of these equilibria in finite and infinite (for MTHPE) games, provide a characterization of the structure of equilibria, and clarify the relationship between the two concepts. Finally, we show how these concepts can be applied in a dynamic model of endogenous club formation. Keywords: voting, agenda-setting games, Markov trembling-hand perfect equilibrium. JEL Classifications: D72, C73.