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This paper explores sensitivity of RTOS kernels in safety-critical systems. We characterize and analyze the consequences of transient faults on key components of the MicroC kernel, a popular RTOS. We specifically focus on its task scheduling and context switching modules. Classes of fault syndromes specific to safety-critical real-time systems are identified. Results reported in this paper demonstrate that 34% of faults led to scheduling dysfunctions. In addition 17% of faults results in system crashes. This represents an important fraction of faults that cannot be ignored during the design phase of safety-critical applications running under an RTOS.