Crest pairing of water surface waves is a consequence of linear dispersion alone and is predicted by the linear Schr¿dinger equation for the slow evolution of a wave train. Linear theory also explains why crest pairing is observed in front of a wave group. The role of nonlinearity is to redistribute sufficient energy to the sidebands such that the linear dispersive mechanism can become effective. There is also quantitative agreement with experimental observations for the propagation of a wave group faster than the linear group velocity. ¿ 1998 American Geophysical Union