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This paper studies higher order sliding-mode-control laws to deal with some spacecraft-attitude-tracking problems. Quasi-continuous second- and third-order sliding controllers and differentiators are applied to quaternion-based spacecraft-attitude-tracking maneuvers. A class of linear sliding manifolds is selected as a function of angular velocities and quaternion errors. The second method of Lyapunov is used to show that tracking is achieved globally. An example of multiaxial attitude-tracking maneuvers is presented, and simulation results are included to verify and compare the practical usefulness of the various controllers.