A flow-mixing calorimeter has been used to measure the excess molar enthalpy H-m(E) of gaseous (ammonia + water) at the mole fraction y = 0.5, at standard atmospheric pressure, and over the temperature range 383.15 K to 493.15 K. The excess molar enthalpy is negative, indicating that the strength of the ammonia-water hydrogen bond is greater than that of the water-water hydrogen bond. The measurements were analysed first in terms of a purely thermodynamic model which assumes that the second virial cross coefficient B-12 and the related isothermal Joule-Thomson coefficient phi(12) are adequately described by an empirical equation of square well form. Information about the strength of the ammonia-water hydrogen bond was obtained by analysing the measurements on the basis of a quasi-chemical association model. It was shown that hydrogen bonding in ammonia is so slight that to use an association model for the second virial coefficient B-11 would be inappropriate. The second virial coefficient B-22 of water was written B-22 = B-22(ns) - R (.) T (.) K-22. The non-specific interaction B-22(ns) between water molecules was calculated from the Stockmayer potential with parameters appropriate to a water-nonpolar fluid interaction, and the specific (hydrogen bonding) forces were described by the association model in terms of an equilibrium constant K-22 (298.15 K) = 0.36 MPa-1 and an enthalpy of formation of DeltaH(22) = -(16.2 +/- 2) kJ (.) mol(-1) for the water-water hydrogen bond. The second virial cross coefficient was written B-12 - B-12(ns) - (R (.) T (.) K-12)/2, and from the temperature dependence of In K 12 the enthalpy of formation of the ammonia-water hydrogen bond was found to be DeltaH(12) = -(19.7 3) kJ - mol-1. and K-12(298.15 K) 0.827 MPa-1. Values of B-12 derived from the measurements are given by the equation: B-12/cm(3 .) mol(-1)) = 38 - 43059 (.) (K/T) - 1.993 (.) exp {1900 (.) (K/T)}.