The dynamics of breaking and structural relaxation of Cl--water, Br--water and water-water hydrogen bonds in aqueous alkali halide solutions are investigated by means of molecular dynamics simulations. The hydrogen bonds are defined by using a set of configurational criteria with respect to the anion(oxygen)oxygen and anion(oxygen)-hydrogen distances and the anion(oxygen)-oxygen -hydrogen angle for an anion(water)-water pair. The results of the hydrogen bond dynamics are obtained for a smaller cutoff and also for a larger cutoff for the angular criterion. In both cases, the dynamics of anion-water hydrogen bonds are found to be slower than that of water-water hydrogen bonds. However, the extent of slowing down is not as great as observed in recent experiments. The relaxation of anion-water hydrogen bonds is found to slow with an increase of ion concentration which is in agreement with the trend observed in experiments. The diffusion coefficients and the orientational relaxation times of water molecules in the vicinity of halide ions and also in the bulk phase are calculated, and the relative changes of these quantities are compared with those of the hydrogen bond dynamics for anion-water and water-water pairs.