Transient performance improvement of adaptive control of a class of single-input single-output (SISO) non-linear systems is considered in this study. The system under study is assumed to be minimum-phase and input-output linearisable. The non-linear dynamics is also assumed to be linearly parameterised in terms of the unknown parameters. The improvement in the transient performance under large parametric uncertainties is obtained with the use of multiple identification models and switching, and the closed loop system is shown to be stable with the switching mechanism. A new methodology is proposed for the quantitative evaluation of the transient performance. The study is verified by simulation of a non-linear physical system.