This article concentrates on the adaptive neural control for switched nonlinear systems interconnected with unmodeled dynamics. The investigated model consists of two dynamic processes, namely, the $x$ -system and the unmodeled $z$ -dynamics. In this article, we focus on a scenario that the unmodeled $z$ -dynamics do not contain input-to-state practically stable (ISpS) modes, that is, all modes are not ISpS (non-ISpS). First, we design an adaptive neural controller such that each mode of the closed-loop $x$ -system is ISpS with respect to the state of dynamic uncertainties. Then, fast average dwell time (fast ADT) and slow average dwell time (slow ADT) are simultaneously used to limit the switching law. In this way, both the closed-loop $x$ -system and the unmodeled $z$ -dynamics are ISpS under switching. By assigning the ISpS gains with small-gain theorem, we can guarantee that the whole closed-loop system is semiglobal uniformly ultimately bounded (SGUUB), and meanwhile, the system output is steered to a small region of zero. Finally, simulation examples are used to verify the effectiveness of the proposed control scheme.