Observations of the Galilean satellites with the radar system at the Arecibo Observatory, Puerto Rico, show that their surfaces are highly diffuse scatterers of radio waves of length 12.6 centimeters; spectra of the radar echoes are asymmetric and broad. The geometric radar albedos for the outer three satellites-0.42 +/- 0.10, 0.20 +/- 0.05, and 0.09 +/- 0.02 for Europa, Ganymede, and Callisto, respectively-show about the same relative decreases as do the optical albedos, although the latter presumably bear only on material much nearer the surface. Radii of 1420 +/- 30, 2640 +/- 80, and 2360 +/- 70 kilometers for Europa, Ganymede, and Callisto were determined from the radar data and are in good agreement with the corresponding optically derived values. Io, observed successfully only once, appears to have an albedo comparable to Ganymede's, but no radius was estimated for it.