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This article addresses the adaptive control problem for strict-feedback nonlinear time-varying systems with unknown control coefficients and external disturbances. To solve the problem of multiple unknown control coefficients, a new lemma based on a general class of Nussbaum functions rather than a specific Nussbaum function is proposed. By lumping all the time-varying parameters and control coefficients into an augmented time-varying vector, and combining the congelation of variables approach, a robust adaptive controller, without the restriction of the persistent excitation (PE) conditions, is constructed for the systems with external disturbances to guarantee the boundedness of all closed-loop variables. Then, by proper transformation, a novel adaptive control scheme is developed to achieve asymptotic stability for strict-feedback nonlinear time-varying systems without external disturbances. In addition, a tracking control method is acquired from the proposed adaptive control method. Finally, two simulations and an actual experiment demonstrate the applicability of the proposed schemes.