The aim of this work is to control highly non-linear plant by employing adaptive control strategies. It is proposed to identify system structure before parameter estimation takes place, i.e. to identify non-linear forms in the system description in a generalized way before estimating the coefficients of the linear and non-linear components of the system. In order to keep the estimates of the non-linear elements as generalized as possible, a polynomial approximation was used as the non-linear model. tt was proposed that a multivariable quadratic form would provide a reasonable approximation to any non-linearity identified, thus affording a great reduction in computation time for the identification of precise forms and hence providing an on-line capability. A control law was devised which would accept estimates of the non-linear description of the system. The stability of the non-linear controller was investigated under the quadratic regime used for estimation. An extension of Liapunov's indirect method was devised in which the coefficients of the locally approximating linear equations are non-linear, thus the indirect method is extended to indicate the asymptotic stability of a single point in a general region of asymptotic stability. Various simulation studies are shown which use the technique to control models of stable and unstable non-linear systems.