High-capacitance bilayer dielectrics based on atomic-layer-deposited HfO2 and spin-cast epoxy are used with networks of single-walled carbon nanotubes (SWNTs) to enable low-voltage, hysteresis-free, and high-performance thin-film transistors (TFTs) on silicon and flexible plastic substrates. These HfO2-epoxy dielectrics exhibit excellent properties including mechanical flexibility, large capacitance (up to ca. 330 nF cm(-2)), and low leakage current (ca. 10(-8) A cm(-2)); their low-temperature (ca. 150 degrees C) deposition makes them compatible with a range of plastic substrates. Analysis and measurements of these dielectrics as gate insulators in SWNT TFTs illustrate several attractive characteristics for this application. Their compatibility with polymers used for charge-transfer doping of SWNTs is also demonstrated through the fabrication of n-channel SWNT TFTs, low-voltage p-n diodes, and complementary logic gates.