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In this paper, the convergence guaranteed attitude stabilization of underactuated spacecraft using two control torques is investigated. By introducing the (w , z) parameters to describe the attitude motion of the underactuated spacecraft, a unified integrated attitude kinematic and dynamic model is originally derived, based on which the controllers can be directly designed for the two actuated axes. Then, three types of controllers are designed to stabilize the attitude and angular velocity along the two actuated axes to zero in fixed time. After that, it is strictly evaluated that the attitude and angular velocity along the underactuated axis can eventually stabilize to the constant values. In this way, the convergence property of the designed controllers can be guaranteed. The utilized controllers are the fixed-time proportional-differential (PD)-like controller, the fixed-time nonsingular terminal sliding mode (NTSM) controller, and the fixed-time integral sliding mode (ISM) controller, respectively. Among them, the fixed-time ISM controller is best since it is strongly robust against disturbances and has no singularity problem naturally, which overcomes the drawbacks of the fixed-time PD-like controller and the fixed-time NTSM controller simultaneously. Lastly, simulated studies are executed to examine the derived results. [ABSTRACT FROM AUTHOR]