The dynamics of water near the polar headgroups of surfactants in a monolayer adsorbed at the air/water interface is likely to play a decisive role in determining the physical behavior of such organized assemblies. We have carried out an atomistic molecular dynamics (MD) simulation of a monolayer of the anionic surfactant sodium bis(2-ethyl-1-hexyl) sulfosuccinate (aerosol-OT or AOT) adsorbed at the air/water interface. The simulation is performed at room temperature with a surface coverage of that at the critical micelle concentration (78 angstrom(2)/molecule). Detailed analyses of the lifetime dynamics of surfactant-water (SW) and water-water (WW) hydrogen bonds at the interface have been carried out. The nonexponential hydrogen bond lifetime correlation functions have been analyzed by using the formalism of Luzar and Chandler, which allowed identification of the bound states at the interface and quantification of the dynamic equilibrium between bound and quasi-free water molecules, in terms of time-dependent relaxation rates. It is observed that the water molecules present in the first hydration layer form strong hydrogen bonds with the surfactant headgroups and hence have longer lifetimes. Importantly, it is found that the overall relaxation of the SW hydrogen bonds is faster for those water molecules which form two hydrogen bonds with the surfactant headgroups than those forming one such hydrogen bond. Equally interestingly, it is further noticed that water molecules beyond the first hydration layer form weaker hydrogen bonds than pure bulk water.