<p>Aeolian vibrations are a major contributor to fatigue in overhead power transmission lines. These oscillations are commonly controlled using fixed dampers, such as Stockbridge units. Nevertheless, the performance of such dampers strongly depends on proper tuning and placement along the line, which can limit their effectiveness under varying operational conditions. To overcome these limitations, moving vibration absorbers have been proposed as a more adaptable solution. However, despite their promise, existing literature has largely neglected the nonlinear effects introduced by both the wind-induced lift force and the dynamic behavior of the moving vibration absorbers themselves. While prior work has studied either fixed nonlinear absorbers or mobile linear absorbers under wind-induced vibrations, this study, for the first time, combines a nonlinear wind excitation model with four nonlinear dynamic absorber profiles, including two two-way motion profiles, and quantifies vibration suppression under transient wind conditions. The aerodynamic lift due to wind is represented using a nonlinear Van der Pol oscillator, whereas the vibration absorber exhibits a restoring force with a cubic stiffness component. Through numerical simulations, we evaluate the performance of nonlinear vibration absorbers with different motion profiles under resonance conditions. Results indicate that nonlinear moving vibration absorbers are more effective in suppressing transverse vibrations compared to their linear, fixed counterparts, offering a more robust damping mechanism. Furthermore, parametric studies explore the effects of absorber velocity, nonlinear stiffness, and damping ratio on system response. We find that the two two-way motion profile consistently yields the highest energy dissipation efficient, hence, superior vibration suppression. These findings offer new guidelines for the design of advanced damping systems in power transmission lines subjected to wind-induced vibrations.</p>