Radiometry in the 20-μm band of eclipses of each of the four Galilean satellites of Jupiter provides information about the thermal properties of the uppermost surface layers of these bodies. Their thermal inertias are all smaller than those of the Moon or of Mercury; there is no evidence for atmospheres, and where the data are of high quality vertically homogeneous thermal properties are excluded. Numerically computed two-layer models reproduce the observed eclipse curves if the following values are adopted for the thermal inertia [erg cm -2s 1/2 °K -1] and the surface density [gcm -2] of the low-conductivity upper layer: Callisto, (1.1 ± 0. 1) × 10° and 0.11 ± 0.02; Canymede, (1.4 ± 0.2) x 10 4 and 0.15 ± 0.03; Io, (1.3 ± 0.4) × 10 4 and 0.10 ± 0.04. Uncertainties in the variation of temperature with orbital phase preclude a model fit for Europa. Such thermal properties, together with other observational evidence, suggest that the surfaces of these satellites are largely composed of ices. A thin coating of frost provides the upper, low-conductivity layer, while the subsurface material maintains a high thermal conductivity by fusion of a mixture of ice and rock. Difficulties with this model, such as its failure to explain the low albedo of Callisto, are discussed; however, a structure of this type with a discontinuity in thermal properties a few millimeters below the surface appears to be required by the eclipse observations.