Results of ASCA X-ray study of central regions of medium-richness clusters of galaxies are summarized, emphasizing differences between cD and non-cD clusters. The intra-cluster medium (ICM) is likely to consist of two (hot and cool) phases within 100 kpc of a cD galaxy, where the ICM metallicity is also enhanced. In contrast, the ICM in non-cD clusters appears to be isothermal with little metallicity gradient right to the center. The gravitational potential exhibits a hierarchical nesting around cD galaxies, while a total mass-density profile with a central cusp is indicated for a non-cD cluster Abell 1060. The ironmass-to-light ratio of the ICM decreases toward the center in both types of clusters, although it is radially constant in peripheral regions. The silicon-to-iron abundance ratio in the ICM increases with the cluster richness, but remains close to the solar ratio around cD galaxies. These overall results are interpreted without appealing to the popular cooling-flow hypothesis. Instead, an emphasis is put on the halo-in-halo structure formed around cD galaxies.