Issues of differentiation-free multiswitching neuroadaptive tracking control of strict-feedback systems are presented. It mainly consists of a set of nominal adaptive neural network compensators plus an auxiliary switched linear controller that ensures the semiglobally/globally ultimately uniformly bounded stability when the unknown nonlinearities are locally/globally linearly bounded, respectively. In particular, the so-called explosion of complexity is annihilated in two steps. First, a set of first-order low-pass filters are constructed for solving such a problem in the nominal neural compensators. In contrast to most existing dynamic surface control-based schemes, bounded stability of the filter dynamics is ensured by virtue of the localness and hence boundedness of the neural compensators. Separation of controller-filter pairs is thus achieved in this paper. Next, an auxiliary switched linear state feedback control is synthesized to further solve such a problem in the nonneural regions. Besides being differentiation-free, such an approach provides more flexibility for meeting various control objectives at a time. An earlier proposed smooth switching algorithm is also incorporated to tackle the control singularity problem. Finally, simulation works are presented to demonstrate the validity of the proposed scheme.