We present evidence for several non-ice constituents in the surface material of the icy Galilean satellites, using the reflectance spectra returned by the Galileo near infrared mapping spectrometer (NIMS) experiment. Five new absorption features are described at 3.4, 3.88, 4.05, 4.25, and 4.57 μm for Callisto and Ganymede, and some seem to exist for Europa as well. The four absorption bands strong enough to be mapped on Callisto and Ganymede are each spatially distributed in different ways, indicating different materials are responsible for each absorption. The spatial distributions are correlated at the local level in complex ways with surface features and in some cases show global patterns. Suggested candidate spectrally active groups, perhaps within larger molecules, producing the five absorptions include C-H, S-H, SO2, CO2, and C≡N. Organic material like tholins are candidates for the 4.57- and 3.4-μm features. We suggest, based on spectroscopic evidence, that CO2 is present as a form which does not allow rotational modes and that SO2 is present neither as a frost nor a free gas. The CO2, SO2, and perhaps cyanogen (4.57 μm) may be present as very small collections of molecules within the crystal structure, perhaps following models for radiation damage and/or for comet and interstellar grain formation at low temperatures. Some of the dark material on these surfaces may be created by radiation damage of the CO2 and other carbon-bearing species and the formation of graphite. These spectra suggest a complex chemistry within the surface materials and an important role for non-ice materials in the evolution of the satellite surfaces.