Although combustion instabilities of low-emission combustion processes have become a major problem in recent years, the prediction of the stability limits of confined flows with heat release is still in its infancy. The most widely used method for the modeling of complicated thermoacoustic systems is based on linear acoustics and a representation of the system as a network of elements, that is, acoustic multiports. Based on such a network, a linear system of equations is constructed from the transfer matrices of the different elements that serves as the basis for investigating the system dynamics. By employing such a network representation of a simple combustor, predictions of thermoacoustic stability obtained with three different methods of stability analysis are compared in this article. It is found that the commonly employed open-loop stability analysis based on a Bode plot can lead to erroneous results. Similar problems may occur with the analysis of the open-loop gain using a Nyquist diagram, as long as control theory methodology is applied to the thermoacoustic system without modifications. The study reveals that the stability analysis of combustors using these methods does not necessarily result in all unstable modes. To overcome this unsatisfactory situation, improved methods have been developed and are presented and validated in a companion article ( Sattelmayer and Polifke, Combustion Science and Technology, vol. 175, pp. 477 497, 2003).