The dynamics of hydrogen bonds between water molecules is probed by means of coherent quasielastic neutron scattering. The choice of appropriate values of the momentum transfer gives information about the time dependence of the DD partial of the scattering function of D₂O. Experimental results demonstrate that the temperature dependence of the dynamics of hydrogen bonds is weak, in contrast with that of the transport properties of liquid water. We discuss our results in view of a recent application of mode coupling theory to describe the dynamics in polymer melts (Richter et al 1998 Physica B 241–243 1005). In particular, we give arguments in favour of a normal (Arrhenius) temperature dependence of hydrogen bond dynamics at extremely low temperatures. We relate this dynamics to β relaxation. This is in contrast to what happens with polymer gels, where the α processes, related to backbone movement, block the molecular motions. The anomalous (non-Arrhenius) temperature dependence of the transport properties of water is therefore due to the increased number of hydrogen bonds, rather then to their intrinsic dynamics, which remains fast.