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This work presents the design of innovative control strategies for a semi-active steering damper aimed at improving two-wheeled vehicles steering stability by controlling the weave and wobble modes. The proposed control strategies arise from a parallelism between steering and vertical dynamics of a motorcycle. According to this parallelism, the Sky-Hook (SH) and Ground-Hook (GH) damping concepts are adapted to the control of steering dynamics. A detailed analysis of the two approaches shows that a tradeoff arises between the damping of wobble and weave mode. It is then shown that the tradeoff can be solved by mixing the SH and GH strategies according to a frequency-range selector. The closed-loop stability properties are investigated via passivity theory. Further, both a multibody simulator and experimental data are employed to validate both the modeling phase and the control strategies performance.