In this article, the problem of global asymptotic stabilisation of non-linear systems is considered. First of all, the global asymptotic stability of a class of non-linear systems is considered. It is proved that the class of non-linear systems is globally asymptotically stable under certain appropriate conditions. Secondly, based on the result obtained, the global asymptotic stabilisation of a class of non-linear systems is investigated, and the feedback control laws, which globally stabilise the class of systems, are designed. Thirdly, by the coordinate change and the results obtained, the global stabilisation of the affine non-linear systems are studied, and then some sufficient conditions of stabilisation are presented. Finally, the global asymptotic stabilisation of partially linear cascade non-linear system is considered. The sufficient conditions of global stabilisation are obtained, and the corresponding feedback control laws, which stabilise the non-linear systems, are designed. In addition, some examples are given to show the effectiveness of the new results.