The starting point for this study was an incident in an industrial plant, where the ammonia synthesis reactor became unstable with rapid temperature oscillations (limit-cycles) in the range from about 300°C to 500°C. A simple dynamic model reproduces this behavior. In industry a steady-state van Heerden analysis is often used to analyze the stability, but a more careful analysis for this reactor system reveals that instability occurs when there still is a positive steady-state margin, namely as a pair of complex conjugate poles cross the imaginary axis (Hopf bifurcation). This is consistent with the obseruations where the instability manifests itself as oscillations rather than extinction of the reaction. This somewhat unusual behavior can be explained by the presence of an inverse response for the temperature response through the reactor beds combined with the positive feedback caused by the preheater.