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In this note, the use of Nussbaum gains for adaptive neural network (NN) control is examined. Extending previous approaches that have been successfully applied to prove the forward completeness property (boundedness up to finite time), we address the boundedness for all time (up to infinity) problem. An example is constructed showing that this is not possible in general with the existing theoretical tools. To achieve boundedness for all time, a novel hysteresis-based deadzone scheme with resetting is introduced for the associated update laws. In this way, a unique, piecewise continuously differentiable solution is obtained while the error converges in finite time within some arbitrarily small region of the origin. Using the proposed modification, an adaptive NN tracking controller is designed for a class of multiple-input multiple-output nonlinear systems.