Measurements of partial 235U(n,2n gamma) gamma-ray cross sections have been carried out as a function of incident neutron energy using the GEANIE spectrometer at LANSCE/WNR+ The yields of gamma rays resulting from the population of discrete levels in the residual nucleus 234U have been measured at incident neutron energies in the 1-20-MeV range. These data provide, with the aid of nuclear reaction modeling, a measurement of the 235U(n,2n) reaction cross section and serve as a proof of principle of the gamma-ray technique for the parallel 23gPu(n,2n) measurement. This paper presents the analysis of the y-ray data and the extraction of partial gamma-ray cross sections as a function of incident neutron energy, Uncertainties associated with the spectroscopic analysis of the data and validation of the results are discussed in detail.