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Power devices based on the wide-bandgap semiconductors SiC and GaN have many potential advantages compared to conventional Si-based switching devices, especially for renewable energy and smart grid applications. However, while these emerging devices have developed rapidly in recent years, many factors affecting their performance and reliability remain unknown. In this paper, we discuss some of the key results that have been obtained for both SiC- and GaN-based devices under Sandia National Lab's “post-Silicon” power electronics reliability program. State-of-the-art, commercially available 4H-SiC MOSFETs are evaluated for stability under high-temperature over-voltage and pulsed over-current conditions. The devices show maximum vulnerability under high-temperature off-state operation at high temperature. The room-temperature pulsed over-current operation results in degradation similar to that observed under high-temperature on-state DC conditions, presumably due to overheating of the device beyond its specified junction temperature. Prototype AlGaN/GaN HEMTs with ~1800 V breakdown are evaluated for stability under different bias conditions. Current collapse is observed and analyzed, and trapping components with very different time constants are found to be involved. The specific nature of degradation and recovery depends strongly upon the particular stress bias (gate vs. drain) condition applied.