The present paper describes finite-gain L₂ stability guaranteed locally by the proposed anti-windup adaptive law for Euler-Lagrange systems with actuator saturation. All constant parameters of the robot system are estimated for an arbitrary target orbit. In order to achieve finite-gain L₂ stability and ensure adaptive tracking performance, an output saturation function of the tracking error is introduced. The finite L₂ gains are derived considering four actuator saturation cases, and finite-gain L₂ stability is guaranteed locally based on passivity. The control performance is verified through numerical simulations using a two-link robot arm.