As part of an observing program using the IUE satellite to investigate the properties of stars within the cores of Galactic globular clusters, we have obtained three spectra of the cluster NGC 1904 (M79). All three were long-integration-time, short-wavelength (SWP) spectra obtained at the so-called 'center-of-light', and all three showed evidence of multiple sources within the IUE large aperture. We describe the analysis of these spectra and present evidence that the UV sources represent individual hot stars in the post-horizontal-branch stage of evolution. We see more UV-bright objects in the core of this cluster than expected from surveys of similar objects discovered in the outer regions of other globulars, leading us to conclude that dynamical effects in the core may significantly alter the path of evolution off the horizontal branch. The spectra also appear to be fitted more closely by models using Population I metal abundances than by Population II abundance models.