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Cylindrical magnetic nanowires (NWs) constitute a viable component of 3D nanoscale magnetic devices and engineering their response to external stimuli is necessary for their future functionalization. Here, by means of micromagnetic simulations, we study the dynamical response of vortex–antivortex and Bloch point domain walls under the action of an applied magnetic field in curved arc-shaped NWs varying the saturation magnetization value. Our results provide evidence that, in the range considered in this work, the curvature has no influence on the critical diameters, delimiting different domain wall types. However, it has a relevant effect on the domain wall dynamics. Specifically, the vortex–antivortex domain wall oscillates back and forth while rotating around the nanowire, and the frequency and amplitude can be tuned by curvature and applied field. On the contrary, Bloch point domain wall dynamics does not show any oscillatory behavior, and the domain wall is rapidly expelled from the nanowire with velocities similar to that of the straight cylindrical nanowires. These results allow engineering magnetic response of cylindrical nanowires with curvature. [ABSTRACT FROM AUTHOR]