We present spectra of Saturn's icy satellites Mimas, Enceladus, Tethys, Dione, Rhea, and Hyperion, 1.0-2.5 µm, with data extending to shorter (Mimas and Enceladus) and longer (Rhea and Dione) wavelengths for certain objects. The spectral resolution (R = λ/ λ) of the data shown here is in the range 800-1000, depending on the specific instrument and configuration used; this is higher than the resolution (R = 225 at 3 µm) afforded by the Visual-Infrared Mapping Spectrometer on the Cassini spacecraft. All of the spectra are dominated by water ice absorption bands and no other features are clearly identified. Spectra of all of these satellites show the characteristic signature of hexagonal H 2 O ice at 1.65 µm. We model the leading hemisphere of Rhea in the wavelength range 0.3-3.6 µm with the Hapke and the Shkuratov radiative transfer codes and discuss the relative merits of the two approaches to fitting the spectrum. In calculations with both codes, the only components used are H 2 O ice, which is the dominant constituent, and a small amount of tholin (Ice Tholin II). Tholin in small quantities (few percent, depending on the mixing mechanism) appears to be an essential component to give the basic red color of the satellite in the region 0.3-1.0 µm. The quantity and mode of mixing of tholin that can produce the intense coloration of Rhea and other icy satellites has bearing on its likely presence in many other icy bodies of the outer Solar System, both of high and low geometric albedos. Using the modeling codes, we also establish detection limits for the ices of CO 2 (a few weight percent, depending on particle size and mixing), CH 4 (same), and NH 4 OH (0.5 weight percent) in our globally averaged spectra of Rhea's leading hemisphere. New laboratory spectral data for NH 4 OH are presented for the purpose of detection on icy bodies. These limits for CO 2 , CH 4 , and NH 4 OH on Rhea are also applicable to the other icy satellites for which spectra are presented here. The reflectance spectrum of Hyperion shows evidence for a broad, unidentified absorption band centered at 1.75 µm.