Nonlinear dynamical systems like thermal hydraulic natural circulation systems can show a very complex behavior under specific conditions. Hence an in-depth analysis of the stability landscape of such systems is necessary. In the field of nuclear reactor technology, the application of advanced system codes, which numerically solve the set of nonlinear partial differential equations describing the underlying system dynamics, is common practice. However, this method is cumbersome and requires large computational effort in order to get an overview of the whole stability landscape of the system. Therefore we are looking for an efficient method which is suitable to reliably provide the solution manifold of the model equations with less computational effort compared to system codes. Here, the application of bifurcation theory together with advanced modeling techniques provides a powerful approach. However, system codes cannot be directly coupled with bifurcation codes due to restrictions of memory and available computation time. Thus an alternative methodology which delivers reliable results with less effort is desirable. An efficient method broadly used in physical and technical fields is the reduction of the system model order by both physically intuitive methods as well as rigorous mathematical optimization principles (Model Order Reduction Theory, MOR). In the paper at hand we demonstrate the application of this technique in the framework of (high-pressure) natural two-phase flow stability analysis. To this end, a well-investigated ROM method, the proper orthogonal decomposition (POD) approach, is selected and the stability of the two-phase flow is investigated by a system code (ATHLET) and a POD-ROM. The objective is to show that the stability behavior for the chosen system states can be calculated by the POD-ROM in a proper agreement with the (validated) system code. These results are the basis to develop a reduced thermal hydraulic model for low pressure conditions, which are not content of this article.