The glassy structure and the primary precipitation phase from supercooled liquid were examined in metal-metal type Zr-, Hf- and Cu-based alloy systems by various advanced analytical techniques. The icosahedral phase precipitates as the primary phase from supercooled liquid for all the metal-metal type glassy alloys examined in the present study. The icosahedral phase has a rhombic triacontahedra type for the Zr-Al-Ni-Cu-NM (NM=Ag, Pd, Au, Pt), Zr-Cu-NM, Hf-Al-Ni-Cu-NM, Cu-Zr-Ti-Pd and Cu-Hf-Ti alloys. In addition, the short-range atomic configurations in their glassy alloys have the features of highly dense packed atomic configuration, new local atomic configurations and long-range homogeneity with attractive interaction. It is therefore concluded that the high glass-forming ability of the metal-metal type alloys is due to the self-formation of the unique glassy structure with the above-described three features which are consistent with the formation of short-range icosahedral atomic configuration.