Stability analysis was performed for Secure Transportable Autonomous Reactor - Liquid Metal (STAR-LM) fast reactor which included the effects of axial thermal conduction through lead bismuth eutectic (LBE) along its direction of flow. The results suggested that fluid axial heat conduction in natural circulation loop should be considered only when the modified Peclet number is in the order of one or below, which is significantly smaller than the practical value (100,000 in the specified loop) of liquid metal natural circulation systems. Therefore, it is appropriate to neglect fluid axial heat conduction effect in the thermal hydraulics analysis related to liquid metal natural circulation cooled nuclear reactors. However, at low heating power conditions, as in the case of reactor start-up or long term cooling after shutdown, fluid axial thermal conduction could become important because of the slow coolant natural circulation. In those cases, the magnitude of the system Peclet number should be closely examined to validate the neglecting of fluid axial heat conduction in natural circulation analysis.