THE precise manner in which quantum-mechanical behaviour at the microscopic level underlies classical behaviour at the macroscopic level remains unclear, despite seventy years of theoretical investigation. Experimentally, the crossover between these regimes can be explored by looking for signatures of quantum-mechanical behaviour-such as tunnelling-in macroscopic systems(1). Magnetic systems (such as small grains, spin glasses and thin films) are often investigated in this way(2-12) because transitions between different magnetic states can be closely monitored. But transitions between states can be induced by thermal fluctuations, as well as by tunnelling, and definitive identification of macroscopic tunnelling events in these complex systems is therefore difficult(13). Here we report the results of low-temperature experiments on a single crystal composed of superparamagnetic manganese clusters (Mn-12-ac), which clearly demonstrate the existence of quantum-mechanical tunnelling of the bulk magnetization. In an applied magnetic field, the magnetization shows hysteresis loops with a distinct ’staircase’ structure : the steps occur at values of the applied field where the energies of different collective spin states of the manganese clusters coincide. At these special values of the held, relaxation from one spin state to another is enhanced above the thermally activated rate by the action of resonant quantum-mechanical tunnelling. These observations corroborate the results of similar experiments performed recently on a system of oriented crystallites made from a powdered sample(4).