GTPase-activating proteins (GAPs) increase the rate of GTP hydrolysis on guanine nucleotide-binding proteins by many orders of magnitude. Studies with Ras and Rho have elucidated the mechanism of GAP action by showing that their catalytic machinery is both stabilized by GAP binding and complemented by the insertion of a so-called 'arginine finger' into the phosphate-binding pocket. This has been proposed as a universal mechanism for GAP-mediated GTP hydrolysis. Ran is a nuclear Ras-related protein that regulates both transport between the nucleus and cytoplasm during interphase, and formation of the mitotic spindle and/or nuclear envelope in dividing cells. Ran-GTP is hydrolysed by the combined action of Ran-binding proteins (RanBPs) and RanGAP. Here we present the three-dimensional structure of a Ran-RanBP1-RanGAP ternary complex in the ground state and in a transition-state mimic. The structure and biochemical experiments show that RanGAP does not act through an arginine finger, that the basic machinery for fast GTP hydrolysis is provided exclusively by Ran and that correct positioning of the catalytic glutamine is essential for catalysis.