In gas phase, collisions that affect the rotational angular momentum lead to the return of the magnetization to its equilibrium (relaxation) in Nuclear Magnetic Resonance (NMR). To the best of our knowledge, the longitudinal relaxation rates R-1 = 1/T-1 of protons in H2O and HDO have never been measured in gas phase. We report R1 in gas phase in a field of 18.8 T, i.e., at a proton Larmor frequency v(0) = 800 MHz, at temperatures between 353 and 373 K and pressures between 9 and 101 kPa. By assuming that spin rotation is the dominant relaxation mechanism, we estimated the effective cross-section sigma(J) for the transfer of angular momentum due to H2O-H2O and HDO-D2O collisions. Our results allow one to test theoretical predictions of the intermolecular potential of water in gas phase.