The differential cross sections for neutron-proton charge-exchange scattering have been measured for mcident neutron momenta between 8 and 29 GeV/c and for four-momentum transfers I tl between 0.002 and 1.0 (GeV/c) 2. A neutron beam with a broad momentum spectrum was scattered from a hquid hydrogen target. The momenta and scattering angles of the forward-scattered protons were measured by a spark-chamber magnet spectrometer. The flight times and scattering angles of the recoil neutrons were measured by a bank of thick scintillation counters. The effic~encles of the neutron counters were determined in a separate measurement. Absolute normalization of the data was obtained from a measurement of the diffracnon dissociation of neutrons from carbon nuclei. Differentml cross sections, based on-23 000 events, are presented for 9 different momenta. The shape of the differential cross sections and the momentum dependence are examined m detail. * We emphasize that even ff there is a significant momentum dependence in the diffraction dissoeiation cross section, it will have very tittle effect on our absolute normalization between 18 and 26 GeV/c, neat the peak in the neutron spectrum.