HYDROGEN bonds play a crucial role in the behaviour of water(1-4); their spatial patterns and fluctuations characterize the structure and dynamics of the liquid(5-7). The processes of breaking and making hydrogen bonds in tile condensed phase can be probed indirectly by a variety of experimental techniques(8), and more quantitative information can be obtained from computer simulations(9). In particular, simulations have revealed that on long timescales the relaxation behaviour of hydrogen bonds in liquid water exhibit non-exponential kinetics(7,10-13), suggesting that bond making and breaking are not simple processes characterized by well defined rate constants. Here we show that these kinetics can be understood in terms of an interplay between diffusion and hydrogen-bond dynamics. In our model, which can be extended to other hydrogen-bonded liquids, diffusion governs whether a specific pair of water molecules are near neighbours, and hydrogen bonds between such pairs form and persist at random with average lifetimes determined by rate constants for bond making and breaking.