NEARLY all of the molecular crystals containing C-60 formed at ambient pressure(1,2) have inter-fullerene separations of the order of 10 Angstrom-the expected distance based on the molecular van der Waals radii. The sole exceptions are the room-temperature phases of AC(60) (where A denotes K, Rb or Cs), which are formed by reversible solid-state transformation from high-temperature (> 150 degrees C) phases(3). These phases have lattice parameters about 9% shorter in one direction, and in addition RbC60 has magnetic properties suggestive of a one-dimensional metal(4). We suggested in ref. 4 that this short distance may be due to covalent bonding between neighbouring C-60 molecules. Here we provide direct evidence for such bonding from powder X-ray diffraction studies of RbC60, and KC60. The linkage is through a [2 + 2] cycloaddition, which has been hypothesized to take place during photopolymerization of solid C-60 (ref. 5), and which has also been proposed(6) for RbC60. Such inter-fullerene linkages are calculated(7,8) to be the preferred mode of dimerization of C-60. The AC(60) phases thus provide an example of a thermal phase transition driven by the reversible formation and breaking of covalent bonds.