Besides their use in separation and filtration processes, ion-exchange membranes have been adopted as electroactive polymer actuators in soft robotics and biomedical engineering, due to their unique coupling between electrochemistry and mechanics. Actuation is generated by the asymmetry in cations and anions transport, as one of the two species is bonded to the membrane backbone, whereas the other can move throughout the membrane. Typically, electrodes are plated on the membrane to enable application of an external electric field. A new, promising contactless actuation configuration for underwater applications consists of immersing a bare membrane in an electrolyte solution, between external electrodes. When an electric field is imposed across the electrodes, a macroscopic bending deformation is observed. Despite major advances in understanding the actuation of cation-exchange membranes (with fixed anions), the actuation of anion-exchange membranes (with fixed cations) is an almost untapped field. In this work, we experimentally investigate the contactless actuation of anion-exchange membranes. In the experiments, we systematically vary the anions in the external solution and inside the membrane, to unravel their effects on membrane actuation. In all tested combinations, the membrane always bends in the opposite direction compared to cation-exchange membranes. Additionally, we find a prominent influence of the external anions on the actuation strength, consistent with previous theories that attribute actuation to solvation effects. Our results help shade light on the chemoelectromechanics of anion-exchange membranes, toward their increase adoption as soft actuators.