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This letter presents the fabrication and characterization of flexible microwave p-intrinsic-n diodes on a plastic substrate employing single-crystal germanium (Ge) nanomembranes. The fabricated flexible device displays high frequency response (e.g., insertion loss smaller than 1.5 dB and isolation larger than 10 dB at frequencies up to 10 GHz). Flexible Ge diodes with various diode structures are modeled and reveal radio frequency (RF) performance tradeoff with device parameters. Furthermore, the flexible Ge diodes show better RF/microwave properties than the flexible Si diodes. The study demonstrates great potential of using flexible active/passive components based on single-crystal Ge nanomembrane for high-performance RF/microwave applications.