A hydrokinetic energy converter using Flow Induced Oscillations (FIOs) of a one-degree-of-freedom cylinder-oscillator, with nonlinear adaptive damping and linear spring stiffness, is introduced and studied experimentally. Comparison to a linear-oscillator in FIO shows that this new converter, with velocity-proportional damping coefficient, is more effective in galloping, where both flow and cylinder speeds are higher. It also impacts VIV, since the converter is no longer restricted by fixed damping, which results either in ceasing motion due to excessive damping, or in low harnessed energy due to insufficient damping. The impact is most profound in the VIV to galloping transition where adaptive damping prevents shutting down of hydrokinetic energy conversion. Damping-to-velocity rate, linear spring-stiffness, and flow-velocity are the experimental parameters with Reynolds number 30,000 <= Re <= 120,000. Experimental results for amplitude response, frequency response, energy harvesting, efficiency and instantaneous energy of the converter are presented and discussed. The main conclusions are: (1) The nonlinear, adaptive, velocity-proportional damping coefficient increases the harnessed power. (2) The operational range of flow velocities increases. (3) At lower flow speeds, the adaptive damping stabilizes the unstable oscillations typically occurring in this region. (4) At higher flow speeds, adaptive damping results in higher harnessed power than constant damping, thus, better emulating passively a corresponding, natural, active motion by fish. (5) Increase of 51%-95% in converted power by the nonlinear oscillator compared to linear oscillator has been measured. (6) The adaptive damping converter reaches a plateau in harnessed efficiency at high flow velocity (fully developed galloping). (C) 2019 Elsevier Ltd. All rights reserved.