NMR relaxation-time measurements have been made from 193° to 374°K on the protons in a sample of ¾ statistical monolayer of water adsorbed on silica gel. Protons in two different environmental states were observed. Proton transfers occur between these two environmental states. For the first time, the T2 value for the longer T2 state has been observed without shortening by nuclear transfers. This longer T2 value increases with temperature in accordance with an activation energy of approximately 7 kcal/mole. The weighted average T1 value has a similar temperature dependence in the range 225° to 270°K. The data were analyzed in detail by use of previously developed theory. Near room temperature, the activation energy for proton transfer is 4.9 kcal/mole, and the average lifetime of a proton in a given state is a few milliseconds. The protons in both states experience very rapid motion; one of the states has an additional slow motion.