<p>This paper presents the results of an investigation into the sensitivity of Weighted Goal Programs (WGPs) and Extended Goal Programs (EGPs) to the choice of their parameters. It discusses how sensitivity might be measured and formally defines the sensitivity of WGPs to the choice of the weights given to each goal and the sensitivity of EGPs to the choice of the parameter alpha, which governs the relative importance given to balancing and optimising in an EGP model. It shows that these sensitivities vary significantly between different standard goal programming models and then examines the sensitivity of very general theoretical WGPs and EGPs. It demonstrates the links between these sensitivities and the structure of a goal programme with the aim of predicting such sensitivity <i>a priori</i>. The paper concludes with a discussion of the reasons for these links and outlines some possible further work.</p>