Here we present models of hot neutron star (NS) atmospheres consisting of thermonuclear ashes of various chemical compositions. These models are essential for studying thermonuclear flashes in X-ray-bursting NSs in which nuclear-burning ashes are transported to the stellar surface. We consider four different mixtures, each dominated by helium, chromium, iron, or nickel. In addition to the opacity sources previously used in NS atmosphere modeling, we include photoionization from excited ionic states as well as approximately 5000 spectral lines. We also developed a method that enables the simultaneous treatment of Compton scattering and a large number of spectral lines. A key feature of the modeled NS atmospheres is the presence of a layer in the transition region between the optically thin and optically thick parts of the atmosphere where the radiation-pressure force increases significantly. This enhanced force sets an upper limit on the maximum attainable bolometric flux for a given surface gravity and chemical composition. The emergent spectra from the computed atmospheres display pronounced absorption edges, whose energies are determined by the dominant chemical species. We fit the model spectra using a diluted blackbody modified by a single absorption edge, and we investigate how the fit parameters depend on both the relative bolometric flux and the chemical composition of the atmosphere. Finally, we discuss constraints on these models imposed by the properties of X-ray bursts that exhibit absorption edges in their spectra, as observed in the systems HETE J1900.1−2455 and GRS 1747−312.