Using high-resolution Galileo images, we counted the number of craters (larger than 1 km) on two of Jupiter's satellites—Callisto (outside and inside the Asgard impact basin) and Ganymede (in the dark cratered Galileo region)—and classified these craters morphologically. Based on the degree of preservation of crater rims, three morphological classes, A, B, and C (from the most preserved to the most degraded), have been identified. The A : B : C ratios, equal, respectively, to 1 : 3 : 5, 1 : 3 : 7, and 1 : 2.5 : 6.5 for fragments of the territory outside and inside the Asgard basin and within Galileo Regio, indicate that these crater populations reached a considerably high degree of maturity. The degradation of kilometer-scale craters on Callisto proceeds by the narrowing of their rims and their disintegration into chains of knobs, probably due to the sublimation of ice that composes the rim material. Comparing the density of craters of different classes in the regions inside and outside Asgard shows that class A craters on the territories examined were formed after the event that formed this impact basin. Kilometer-scale craters on Ganymede degrade through the expansion and smoothing of their rims and the dissection of them by radial furrows. This implies the involvement in the crater destruction of a downslope movement triggered by the seismic activity that accompanied the formation of tectonic grooves. It is possible that ice sublimation also took part in the destruction of craters on Ganymede, but its effect was less prominent than the effect of downslope movements.