Large-area, free-standing and single-crystalline GaN nanomembranes are prepared by electrochemical etching from epitaxial layers. As-prepared nanomembranes are highly resistive but can become electronically active upon optical excitation, with an excellent electron mobility. The interaction of excited carriers with surface states is investigated by intensity-dependent photoconductivity gain and temperature-dependent photocurrent decay. Normally off enhancement-type GaN nanomembrane MOS transistors are demonstrated, suggesting that GaN could be used in flexible electronics for high power and high frequency applications.