A method is proposed for determining the stability of a non linear systemby means of comparison with another linear or non linear stable system whose trajectories are known. The comparison utilises the geometric interpretation of Liapounov's second method. A Liapounov function is used, defined by the solution of a proper “auxiliary system” of differential equations: the trajectory defined by the solution is not required to be closed. Moreover, an approximate evaluation of asymptotic stability region is proposed. Examples are given, concerning second order systems with one or two non linearities.