IRK1 (Kir2.1) inward-rectifier K+ channels exhibit exceedingly steep rectification, which reflects strong voltage dependence of channel block by intracellular cations such as the polyamine spermine. On the basis of studies of IRK1 block by various amine blockers, it was proposed that the observed voltage dependence (valence approximately 5) of IRK1 block by spermine results primarily from K+ ions, not spermine itself, traversing the transmembrane electrical field that drops mostly across the narrow ion selectivity filter, as spermine and K+ ions displace one another during channel block and unblock. If indeed spermine itself only rarely penetrates deep into the ion selectivity filter, then a long blocker with head groups much wider than the selectivity filter should exhibit comparably strong voltage dependence. We confirm here that channel block by two molecules of comparable length, decane-bis-trimethylammonium (bis-QA(C10)) and spermine, exhibit practically identical overall voltage dependence even though the head groups of the former are much wider ( approximately 6 A) than the ion selectivity filter ( approximately 3 A). For both blockers, the overall equilibrium dissociation constant differs from the ratio of apparent rate constants of channel unblock and block. Also, although steady-state IRK1 block by both cations is strongly voltage dependent, their apparent channel-blocking rate constant exhibits minimal voltage dependence, which suggests that the pore becomes blocked as soon as the blocker encounters the innermost K+ ion. These findings strongly suggest the existence of at least two (potentially identifiable) sequentially related blocked states with increasing numbers of K+ ions displaced. Consequently, the steady-state voltage dependence of IRK1 block by spermine or bis-QA(C10) should increase with membrane depolarization, a prediction indeed observed. Further kinetic analysis identifies two blocked states, and shows that most of the observed steady-state voltage dependence is associated with the transition between blocked states, consistent with the view that the mutual displacement of blocker and K+ ions must occur mainly as the blocker travels along the long inner pore.