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An account is presented of our studies of the order-disorder phase transitions in KSCN, RbSCN, and CsSCN. These are based on parameter-free interionic potentials based on the Gordon-Kim modified electron gas formalism extended to molecular ions. We performed static structural relaxations and supercell molecular dynamics and predicted with reasonable accuracy the temperatures for the onset of the transitions. In particular, we address the question of how the SCN- ions disorder to yield subsequent structural transformations. We found high-temperature phases of average Fm3m symmetry for both KSCN and RbSCN. We argue that in reality the full appearance of these phases is preempted by melting. However, they are candidates for the twin boundaries which are observed in the high-temperature “average” tetragonal phases. The high-temperature phase of CsSCN was found to be of average Fm3m symmetry.