In the paper, analysis of stabilised output-error methods (SOEMs) for parameter estimation of unstable aircraft is presented. These methods overcome the numerical difficulties encountered in parameter estimation of unstable systems by utilising measured states. The methods, along with the output error method (OEM) and the equation error method (EEM), are briefly described for the sake of comparison. However, the main idea of the paper is to present asymptotic analysis of the SOEM. The results of application of SOEMs to simulated data of an unstable/augmented aircraft are presented.