Natural materials are renowned for their strength and toughness^1,2,3,4,5. Spider dragline silk has a breakage energy per unit weight two orders of magnitude greater than high tensile steel^1,6, and is representative of many other strong natural fibres^3,7,8. The abalone shell, a composite of calcium carbonate plates sandwiched between organic material, is 3,000 times more fracture resistant than a single crystal of the pure mineral^4,5. The organic component, comprising just a few per cent of the composite by weight⁹, is thought to hold the key to nacre's fracture toughness^10,11. Ceramics laminated with organic material are more fracture resistant than non-laminated ceramics^11,12, but synthetic materials made of interlocking ceramic tablets bound by a few weight per cent of ordinary adhesives do not have a toughness comparable to nacre¹³. We believe that the key to nacre's fracture resistance resides in the polymer adhesive, and here we reveal the properties of this adhesive by using the atomic force microscope¹⁴ to stretch the organic molecules exposed on the surface of freshly cleaved nacre. The adhesive fibres elongate in a stepwise manner as folded domains or loops are pulled open. The elongation events occur for forces of a few hundred piconewtons, which are smaller than the forces of over a nanonewton required to break the polymer backbone in the threads. We suggest that this ‘modular’ elongation mechanism might prove to be quite general for conveying toughness to natural fibres and adhesives, and we predict that it might be found also in dragline silk.