Natural circulation with two-phase flow is a nonlinear dynamical systems, which can show a very complex and strange behavior under specific conditions. The application of stability analysis requires a large computational effort and is cumbersome in case of prediction the dynamical behavior by system codes alone. Therefore, model-order reduction techniques are used to compensate this disadvantage by coupling with a bifurcation code such as MatCont. A reduced-order model is derived by employing the proper orthogonal decomposition (POD) to analyze the stability landscape of a low pressure natural circulation system representing passive safety systems such as the containment cooling condenser. The required full-order model contains a classical natural circulation loop with a heated section and a riser. The two-phase region is modeled by a drift–flux mixture model. The reliability of the full-order model is investigated by comparison with a reference model by the validated system code ATHLET.