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Many biological and physiological processes depend upon directed migration of cells, which is typically mediated by chemical or physical gradients. However, conventional chemical or physical gradients have finite dynamic range and can therefore operate only over limited distances. Cells can overcome this limitation by relaying chemotactic signals, but chemical relay of directional information requires intricate orchestration of timing of signals. Nanotopographies that are on a comparable length scale with the features in the extracellular matrix offer an option to guide cells over large distances without a global gradient. Here I show that both cell motion and actin-wave propagation in Dictyostelium discoideum (D. discoideum) are guided bidirectionally on nanoridges/nanogrooves. The guidance efficiency depends on the ridge spacing. Actin polymerization preferentially occurs around individual ridges, giving rise to coupled actin streaks on the opposite sides of a single ridge. Cells can be guided in a single preferred direction based solely on local asymmetries in nanosawteeth on subcellular scales, which can be repeated over arbitrarily large areas, providing directional guidance over an unlimited distance. The direction and strength of the guidance is sensitive to the details of the nanosawteeth, suggesting that this phenomenon plays a context-dependent role in vivo. I demonstrate that asymmetric nanosawteeth guide the direction of internal actin polymerization waves, and that cells move in the same direction as these waves. This phenomenon is observed both for the pseudopod-dominated migration of the amoeboid D. discoideum and for the lamellipod-driven migration of human neutrophils. The conservation of this mechanism across cell types and the asymmetric shape of many natural scaffolds suggest that actin-wave-based guidance is important in biology and physiology. Even symmetric nanotopographies can induce unidirectional bias in actin-wave propagation and cell motion. This bias presumably originates from the intrinsic actin chirality. A counterclockwise bias in both cell motion and actin-wave propagation is observed in D. discoideum migrating on 0.8-μm-spaced nanorings and in neutrophils migrating on 2-μm-spaced nanorings. The different effects of ring spacing on guidance efficiency between D. discoideum and neutrophils may arise from the difference in the ultrastructure of the actin network between those two cell types.